{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python Flight Mechanics Engine "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This installs `pyfme` to be run in this online notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install git+https://github.com/AeroPython/PyFME.git"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Aircraft "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to perform a simulation, the first thing we need is an aircraft:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.aircrafts import Cessna172"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "aircraft = Cessna172()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aircraft will provide the simulator the forces, moments and inertial properties in order to perform the integration of the dynamic system equations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Aircraft mass: 1043.2616 kg\n",
      "Aircraft inertia tensor: \n",
      " [[ 1285.3154166      0.             0.        ]\n",
      " [    0.          1824.9309607      0.        ]\n",
      " [    0.             0.          2666.89390765]] kg/m²\n"
     ]
    }
   ],
   "source": [
    "print(f\"Aircraft mass: {aircraft.mass} kg\")\n",
    "print(f\"Aircraft inertia tensor: \\n {aircraft.inertia} kg/m²\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "forces: [ 0.  0.  0.] N\n",
      "moments: [ 0.  0.  0.] N·m\n"
     ]
    }
   ],
   "source": [
    "print(f\"forces: {aircraft.total_forces} N\")\n",
    "print(f\"moments: {aircraft.total_moments} N·m\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the aircraft, in order to calculate its forces and moments it is necessary to set the controls values within the limits: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0}\n"
     ]
    }
   ],
   "source": [
    "print(aircraft.controls)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'delta_elevator': (-0.4537856055185257, 0.48869219055841229), 'delta_aileron': (-0.26179938779914941, 0.3490658503988659), 'delta_rudder': (-0.27925268031909273, 0.27925268031909273), 'delta_t': (0, 1)}\n"
     ]
    }
   ],
   "source": [
    "print(aircraft.control_limits)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "but also to provide and environment (ie. atmosphere, winds, gravity) and the aircraft state, which will also determine the aerodynamic contribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Environment "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.environment.atmosphere import ISA1976\n",
    "from pyfme.environment.wind import NoWind\n",
    "from pyfme.environment.gravity import VerticalConstant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "atmosphere = ISA1976()\n",
    "gravity = VerticalConstant()\n",
    "wind = NoWind()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The atmosphere, wind and gravity model make up the environment:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.environment import Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "environment = Environment(atmosphere, gravity, wind)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The environment has an update method which given the state (ie. position, altitude...) updates the environment variables (ie. density, wind magnitude, gravity force...)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on method update in module pyfme.environment.environment:\n",
      "\n",
      "update(state) method of pyfme.environment.environment.Environment instance\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(environment.update)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even if the state can be set manually by giving the position, attitude, velocity, angular velocities... Most of the times, the user will want to trim the aircraft in a stationary condition. The aircraft controls to flight in that condition will be also provided by the trimmer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.utils.trimmer import steady_state_trim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Help on function steady_state_trim in module pyfme.utils.trimmer:\n",
      "\n",
      "steady_state_trim(aircraft, environment, pos, psi, TAS, controls, gamma=0, turn_rate=0, exclude=None, verbose=0)\n",
      "    Finds a combination of values of the state and control variables\n",
      "    that correspond to a steady-state flight condition.\n",
      "    \n",
      "    Steady-state aircraft flight is defined as a condition in which all\n",
      "    of the motion variables are constant or zero. That is, the linear and\n",
      "    angular velocity components are constant (or zero), thus all\n",
      "     acceleration components are zero.\n",
      "    \n",
      "    Parameters\n",
      "    ----------\n",
      "    aircraft : Aircraft\n",
      "        Aircraft to be trimmed.\n",
      "    environment : Environment\n",
      "        Environment where the aircraft is trimmed including atmosphere,\n",
      "        gravity and wind.\n",
      "    pos : Position\n",
      "        Initial position of the aircraft.\n",
      "    psi : float, opt\n",
      "        Initial yaw angle (rad).\n",
      "    TAS : float\n",
      "        True Air Speed (m/s).\n",
      "    controls : dict\n",
      "        Initial value guess for each control or fixed value if control is\n",
      "        included in exclude.\n",
      "    gamma : float, optional\n",
      "        Flight path angle (rad).\n",
      "    turn_rate : float, optional\n",
      "        Turn rate, d(psi)/dt (rad/s).\n",
      "    exclude : list, optional\n",
      "        List with controls not to be trimmed. If not given, every control\n",
      "        is considered in the trim process.\n",
      "    verbose : {0, 1, 2}, optional\n",
      "        Level of least_squares verbosity:\n",
      "            * 0 (default) : work silently.\n",
      "            * 1 : display a termination report.\n",
      "            * 2 : display progress during iterations (not supported by 'lm'\n",
      "              method).\n",
      "    \n",
      "    Returns\n",
      "    -------\n",
      "    state : AircraftState\n",
      "        Trimmed aircraft state.\n",
      "    trimmed_controls : dict\n",
      "        Trimmed aircraft controls\n",
      "    \n",
      "    Notes\n",
      "    -----\n",
      "    See section 3.4 in [1] for the algorithm description.\n",
      "    See section 2.5 in [1] for the definition of steady-state flight\n",
      "    condition.\n",
      "    \n",
      "    References\n",
      "    ----------\n",
      "    .. [1] Stevens, BL and Lewis, FL, \"Aircraft Control and Simulation\",\n",
      "        Wiley-lnterscience.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "help(steady_state_trim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.models.state.position import EarthPosition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "pos = EarthPosition(x=0, y=0, height=1000)\n",
    "psi = 0.5  # rad\n",
    "TAS = 45  # m/s\n",
    "controls0 = {'delta_elevator': 0, 'delta_aileron': 0, 'delta_rudder': 0, 'delta_t': 0.5}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "trimmed_state, trimmed_controls = steady_state_trim(\n",
    "    aircraft,\n",
    "    environment,\n",
    "    pos,\n",
    "    psi,\n",
    "    TAS,\n",
    "    controls0\n",
    ")    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Aircraft State \n",
       "x_e: 0.00 m, y_e: 0.00 m, z_e: -1000.00 m \n",
       "theta: 0.076 rad, phi: 0.000 rad, psi: 0.500 rad \n",
       "u: 44.87 m/s, v: 0.00 m/s, w: 3.40 m/s \n",
       "P: 0.00 rad/s, Q: 0.00 rad/s, R: 0.00 rad/s \n",
       "u_dot: 0.00 m/s², v_dot: -0.00 m/s², w_dot: 0.00 m/s² \n",
       "P_dot: 0.00 rad/s², Q_dot: -0.00 rad/s², R_dot: 0.00 rad/s² "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trimmed_state"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'delta_aileron': 2.4925251333542672e-18,\n",
       " 'delta_elevator': -0.048951124635247797,\n",
       " 'delta_rudder': -1.0367511099559949e-17,\n",
       " 'delta_t': 0.57799667845248515}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trimmed_controls"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, all the necessary elements in order to calculate forces and moments are available "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Environment conditions for the current state:\n",
    "environment.update(trimmed_state)\n",
    "\n",
    "# Forces and moments calculation:\n",
    "forces, moments = aircraft.calculate_forces_and_moments(trimmed_state, environment, controls0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.68256520e-11,  -1.49629613e-18,   2.36468622e-11]),\n",
       " array([  3.03652088e-14,  -1.54951943e-11,   3.06443592e-14]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "forces, moments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The aircraft is trimmed indeed: the total forces and moments (aerodynamics + gravity + thrust) are zero"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to simulate the dynamics of the aircraft under certain inputs in an environment, the user can set up a simulation using a dynamic system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.models import EulerFlatEarth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "system = EulerFlatEarth(t0=0, full_state=trimmed_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Constant Controls "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.utils.input_generator import Constant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "controls = controls = {\n",
    "    'delta_elevator': Constant(trimmed_controls['delta_elevator']),\n",
    "    'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n",
    "    'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n",
    "    'delta_t': Constant(trimmed_controls['delta_t'])\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.simulator import Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = Simulation(aircraft, system, environment, controls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the simulation is set, the propagation can be performed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "time: 100%|█████████▉| 9.999999999999831/10 [00:05<00:00,  1.91it/s]  \n"
     ]
    }
   ],
   "source": [
    "results = sim.propagate(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The results are returned in a DataFrame:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Fx</th>\n",
       "      <th>Fy</th>\n",
       "      <th>Fz</th>\n",
       "      <th>Mach</th>\n",
       "      <th>Mx</th>\n",
       "      <th>My</th>\n",
       "      <th>Mz</th>\n",
       "      <th>TAS</th>\n",
       "      <th>a</th>\n",
       "      <th>aileron</th>\n",
       "      <th>...</th>\n",
       "      <th>thrust</th>\n",
       "      <th>u</th>\n",
       "      <th>v</th>\n",
       "      <th>v_down</th>\n",
       "      <th>v_east</th>\n",
       "      <th>v_north</th>\n",
       "      <th>w</th>\n",
       "      <th>x_earth</th>\n",
       "      <th>y_earth</th>\n",
       "      <th>z_earth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.01</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>3.988299e-17</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.931208e-14</td>\n",
       "      <td>-1.502423e-11</td>\n",
       "      <td>3.036133e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.373417e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.02</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>1.113008e-16</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.830690e-14</td>\n",
       "      <td>-1.456759e-11</td>\n",
       "      <td>3.008343e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.372773e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.03</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>2.118543e-16</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.734757e-14</td>\n",
       "      <td>-1.412482e-11</td>\n",
       "      <td>2.981037e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.371706e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.04</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>3.406791e-16</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.643204e-14</td>\n",
       "      <td>-1.369551e-11</td>\n",
       "      <td>2.954186e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.370221e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.05</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>4.969478e-16</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.555839e-14</td>\n",
       "      <td>-1.327925e-11</td>\n",
       "      <td>2.927764e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.368322e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.06</th>\n",
       "      <td>1.671197e-11</td>\n",
       "      <td>6.798681e-16</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.472474e-14</td>\n",
       "      <td>-1.287564e-11</td>\n",
       "      <td>2.901745e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.366015e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.07</th>\n",
       "      <td>1.671197e-11</td>\n",
       "      <td>8.886811e-16</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.392932e-14</td>\n",
       "      <td>-1.248430e-11</td>\n",
       "      <td>2.876107e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.363303e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.08</th>\n",
       "      <td>1.671197e-11</td>\n",
       "      <td>1.122661e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.317044e-14</td>\n",
       "      <td>-1.210485e-11</td>\n",
       "      <td>2.850826e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.360192e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.09</th>\n",
       "      <td>1.671197e-11</td>\n",
       "      <td>1.381110e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.244646e-14</td>\n",
       "      <td>-1.173694e-11</td>\n",
       "      <td>2.825879e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.356686e-16</td>\n",
       "      <td>4.440892e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.10</th>\n",
       "      <td>1.682565e-11</td>\n",
       "      <td>1.663364e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.175583e-14</td>\n",
       "      <td>-1.138021e-11</td>\n",
       "      <td>2.801248e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.352790e-16</td>\n",
       "      <td>8.881784e-16</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.11</th>\n",
       "      <td>1.705303e-11</td>\n",
       "      <td>1.968783e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.109706e-14</td>\n",
       "      <td>-1.103432e-11</td>\n",
       "      <td>2.776911e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.348508e-16</td>\n",
       "      <td>1.776357e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.12</th>\n",
       "      <td>1.716671e-11</td>\n",
       "      <td>2.296755e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.046872e-14</td>\n",
       "      <td>-1.069894e-11</td>\n",
       "      <td>2.752851e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.343846e-16</td>\n",
       "      <td>2.220446e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.13</th>\n",
       "      <td>1.728040e-11</td>\n",
       "      <td>2.646694e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.986945e-14</td>\n",
       "      <td>-1.037376e-11</td>\n",
       "      <td>2.729050e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.338806e-16</td>\n",
       "      <td>2.664535e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.14</th>\n",
       "      <td>1.739409e-11</td>\n",
       "      <td>3.018038e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.929794e-14</td>\n",
       "      <td>-1.005846e-11</td>\n",
       "      <td>2.705491e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.333395e-16</td>\n",
       "      <td>3.552714e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.15</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>3.410248e-15</td>\n",
       "      <td>2.546585e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.875295e-14</td>\n",
       "      <td>-9.752741e-12</td>\n",
       "      <td>2.682158e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.327615e-16</td>\n",
       "      <td>3.996803e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.16</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>3.816426e-15</td>\n",
       "      <td>2.728484e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.819868e-14</td>\n",
       "      <td>-9.079912e-12</td>\n",
       "      <td>-7.014492e-16</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.321473e-16</td>\n",
       "      <td>4.440892e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.17</th>\n",
       "      <td>1.773515e-11</td>\n",
       "      <td>4.196172e-15</td>\n",
       "      <td>2.728484e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.744420e-14</td>\n",
       "      <td>-8.803938e-12</td>\n",
       "      <td>-8.500321e-16</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.315258e-16</td>\n",
       "      <td>4.440892e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>6</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.18</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>4.585643e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.670343e-14</td>\n",
       "      <td>-8.156199e-12</td>\n",
       "      <td>8.450127e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.309147e-16</td>\n",
       "      <td>4.440892e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>7</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.19</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>5.007389e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.609528e-14</td>\n",
       "      <td>-7.147997e-12</td>\n",
       "      <td>1.098344e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.303082e-16</td>\n",
       "      <td>4.884981e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.20</th>\n",
       "      <td>1.784883e-11</td>\n",
       "      <td>5.449073e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.554361e-14</td>\n",
       "      <td>-6.930741e-12</td>\n",
       "      <td>1.081493e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.296945e-16</td>\n",
       "      <td>4.884981e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.21</th>\n",
       "      <td>1.784883e-11</td>\n",
       "      <td>5.904860e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.501568e-14</td>\n",
       "      <td>-6.720088e-12</td>\n",
       "      <td>1.064987e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.290711e-16</td>\n",
       "      <td>5.329071e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.22</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>6.378532e-15</td>\n",
       "      <td>3.456080e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.453281e-14</td>\n",
       "      <td>-6.143234e-12</td>\n",
       "      <td>1.553733e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.284374e-16</td>\n",
       "      <td>5.329071e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>8</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.23</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>6.868901e-15</td>\n",
       "      <td>3.456080e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.408436e-14</td>\n",
       "      <td>-5.576365e-12</td>\n",
       "      <td>2.210854e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.277876e-16</td>\n",
       "      <td>5.329071e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>9</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.24</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>7.388058e-15</td>\n",
       "      <td>3.637979e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.373220e-14</td>\n",
       "      <td>-5.406877e-12</td>\n",
       "      <td>2.191748e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.271166e-16</td>\n",
       "      <td>5.773160e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.25</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>7.912658e-15</td>\n",
       "      <td>3.819878e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.334583e-14</td>\n",
       "      <td>-4.869937e-12</td>\n",
       "      <td>1.028275e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.264191e-16</td>\n",
       "      <td>5.773160e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.26</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>8.435388e-15</td>\n",
       "      <td>4.001777e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.290080e-14</td>\n",
       "      <td>-4.341769e-12</td>\n",
       "      <td>1.957141e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.257109e-16</td>\n",
       "      <td>6.217249e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.27</th>\n",
       "      <td>1.773515e-11</td>\n",
       "      <td>8.990677e-15</td>\n",
       "      <td>4.001777e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.258186e-14</td>\n",
       "      <td>-4.209805e-12</td>\n",
       "      <td>1.939235e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.249888e-16</td>\n",
       "      <td>6.217249e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>10</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.28</th>\n",
       "      <td>1.750777e-11</td>\n",
       "      <td>9.568884e-15</td>\n",
       "      <td>4.183676e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.232674e-14</td>\n",
       "      <td>-3.709249e-12</td>\n",
       "      <td>3.032277e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.242409e-16</td>\n",
       "      <td>6.217249e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.29</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>1.017752e-14</td>\n",
       "      <td>4.365575e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.216324e-14</td>\n",
       "      <td>-3.216358e-12</td>\n",
       "      <td>1.797171e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.234528e-16</td>\n",
       "      <td>6.661338e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.30</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>1.077698e-14</td>\n",
       "      <td>4.365575e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.188180e-14</td>\n",
       "      <td>-2.738449e-12</td>\n",
       "      <td>1.206311e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.226298e-16</td>\n",
       "      <td>6.661338e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.71</th>\n",
       "      <td>1.496119e-10</td>\n",
       "      <td>9.333875e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.985816e-16</td>\n",
       "      <td>3.356707e-26</td>\n",
       "      <td>7.112137e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.049488e-15</td>\n",
       "      <td>5.906386e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>383</td>\n",
       "      <td>209</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.72</th>\n",
       "      <td>1.497256e-10</td>\n",
       "      <td>9.345363e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.020084e-16</td>\n",
       "      <td>3.222438e-26</td>\n",
       "      <td>7.119961e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.050029e-15</td>\n",
       "      <td>5.910827e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>383</td>\n",
       "      <td>209</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.73</th>\n",
       "      <td>1.498393e-10</td>\n",
       "      <td>9.356856e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.054401e-16</td>\n",
       "      <td>3.088170e-26</td>\n",
       "      <td>7.127691e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.050570e-15</td>\n",
       "      <td>5.919709e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>384</td>\n",
       "      <td>209</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.74</th>\n",
       "      <td>1.500666e-10</td>\n",
       "      <td>9.368356e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.088762e-16</td>\n",
       "      <td>3.088170e-26</td>\n",
       "      <td>7.135326e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.051109e-15</td>\n",
       "      <td>5.924150e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>384</td>\n",
       "      <td>210</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.75</th>\n",
       "      <td>1.501803e-10</td>\n",
       "      <td>9.379861e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.123162e-16</td>\n",
       "      <td>2.953902e-26</td>\n",
       "      <td>7.142868e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.051648e-15</td>\n",
       "      <td>5.933032e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>385</td>\n",
       "      <td>210</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.76</th>\n",
       "      <td>1.502940e-10</td>\n",
       "      <td>9.391371e-13</td>\n",
       "      <td>6.366463e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.157596e-16</td>\n",
       "      <td>2.819634e-26</td>\n",
       "      <td>7.150315e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.052185e-15</td>\n",
       "      <td>5.937473e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>385</td>\n",
       "      <td>210</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.77</th>\n",
       "      <td>1.504077e-10</td>\n",
       "      <td>9.402888e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.192060e-16</td>\n",
       "      <td>2.551097e-26</td>\n",
       "      <td>7.157668e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.052722e-15</td>\n",
       "      <td>5.946355e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>385</td>\n",
       "      <td>210</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.78</th>\n",
       "      <td>1.505214e-10</td>\n",
       "      <td>9.414411e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.226548e-16</td>\n",
       "      <td>2.551097e-26</td>\n",
       "      <td>7.164927e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.053258e-15</td>\n",
       "      <td>5.955236e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>386</td>\n",
       "      <td>210</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.79</th>\n",
       "      <td>1.505214e-10</td>\n",
       "      <td>9.425939e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.261057e-16</td>\n",
       "      <td>2.416829e-26</td>\n",
       "      <td>7.172090e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.053792e-15</td>\n",
       "      <td>5.955236e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>386</td>\n",
       "      <td>211</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.80</th>\n",
       "      <td>1.507487e-10</td>\n",
       "      <td>9.437473e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.295581e-16</td>\n",
       "      <td>2.282561e-26</td>\n",
       "      <td>7.179160e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.054326e-15</td>\n",
       "      <td>5.959677e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>387</td>\n",
       "      <td>211</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.81</th>\n",
       "      <td>1.508624e-10</td>\n",
       "      <td>9.449014e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.330116e-16</td>\n",
       "      <td>2.148292e-26</td>\n",
       "      <td>7.186134e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.054859e-15</td>\n",
       "      <td>5.968559e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>387</td>\n",
       "      <td>211</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.82</th>\n",
       "      <td>1.509761e-10</td>\n",
       "      <td>9.460560e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.364657e-16</td>\n",
       "      <td>2.014024e-26</td>\n",
       "      <td>7.193015e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.055391e-15</td>\n",
       "      <td>5.973000e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>387</td>\n",
       "      <td>211</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.83</th>\n",
       "      <td>1.510898e-10</td>\n",
       "      <td>9.472112e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.399199e-16</td>\n",
       "      <td>2.014024e-26</td>\n",
       "      <td>7.199800e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.055922e-15</td>\n",
       "      <td>5.977441e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>388</td>\n",
       "      <td>212</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.84</th>\n",
       "      <td>1.513172e-10</td>\n",
       "      <td>9.483671e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.433738e-16</td>\n",
       "      <td>1.879756e-26</td>\n",
       "      <td>7.206491e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.056453e-15</td>\n",
       "      <td>5.986323e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>388</td>\n",
       "      <td>212</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.85</th>\n",
       "      <td>1.514309e-10</td>\n",
       "      <td>9.495235e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.468269e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.213087e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.056982e-15</td>\n",
       "      <td>5.990763e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>388</td>\n",
       "      <td>212</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.86</th>\n",
       "      <td>1.515446e-10</td>\n",
       "      <td>9.506806e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.502788e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.219589e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.057510e-15</td>\n",
       "      <td>5.999645e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>389</td>\n",
       "      <td>212</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.87</th>\n",
       "      <td>1.516582e-10</td>\n",
       "      <td>9.518383e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.537290e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.225996e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.058037e-15</td>\n",
       "      <td>6.004086e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>389</td>\n",
       "      <td>212</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.88</th>\n",
       "      <td>1.517719e-10</td>\n",
       "      <td>9.529966e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.571770e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.232309e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.058563e-15</td>\n",
       "      <td>6.008527e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>390</td>\n",
       "      <td>213</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.89</th>\n",
       "      <td>1.521130e-10</td>\n",
       "      <td>9.541555e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.606225e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.238527e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.059089e-15</td>\n",
       "      <td>6.017409e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>390</td>\n",
       "      <td>213</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.90</th>\n",
       "      <td>1.522267e-10</td>\n",
       "      <td>9.553150e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.640649e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.244651e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.059613e-15</td>\n",
       "      <td>6.021850e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>390</td>\n",
       "      <td>213</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.91</th>\n",
       "      <td>1.523404e-10</td>\n",
       "      <td>9.564752e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.675038e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.250681e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.060137e-15</td>\n",
       "      <td>6.030731e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>391</td>\n",
       "      <td>213</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.92</th>\n",
       "      <td>1.524540e-10</td>\n",
       "      <td>9.576360e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.709388e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.256617e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.060659e-15</td>\n",
       "      <td>6.035172e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>391</td>\n",
       "      <td>214</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.93</th>\n",
       "      <td>1.526814e-10</td>\n",
       "      <td>9.587975e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.743695e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.262459e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.061180e-15</td>\n",
       "      <td>6.039613e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>392</td>\n",
       "      <td>214</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.94</th>\n",
       "      <td>1.527951e-10</td>\n",
       "      <td>9.599596e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.777954e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.268207e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.061701e-15</td>\n",
       "      <td>6.048495e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>392</td>\n",
       "      <td>214</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.95</th>\n",
       "      <td>1.529088e-10</td>\n",
       "      <td>9.611223e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.812161e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.273862e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.062220e-15</td>\n",
       "      <td>6.052936e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>392</td>\n",
       "      <td>214</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.96</th>\n",
       "      <td>1.530225e-10</td>\n",
       "      <td>9.622857e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.846312e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.279423e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.062739e-15</td>\n",
       "      <td>6.061818e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>393</td>\n",
       "      <td>214</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.97</th>\n",
       "      <td>1.531362e-10</td>\n",
       "      <td>9.634497e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.880402e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.284891e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.063256e-15</td>\n",
       "      <td>6.066259e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>393</td>\n",
       "      <td>215</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.98</th>\n",
       "      <td>1.533635e-10</td>\n",
       "      <td>9.646144e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.914427e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.290265e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.063773e-15</td>\n",
       "      <td>6.070699e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>394</td>\n",
       "      <td>215</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9.99</th>\n",
       "      <td>1.534772e-10</td>\n",
       "      <td>9.657797e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.948383e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.295547e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.064288e-15</td>\n",
       "      <td>6.079581e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>394</td>\n",
       "      <td>215</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10.00</th>\n",
       "      <td>1.535909e-10</td>\n",
       "      <td>9.669457e-13</td>\n",
       "      <td>6.548362e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>3.982266e-16</td>\n",
       "      <td>1.745487e-26</td>\n",
       "      <td>7.300736e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>1.064803e-15</td>\n",
       "      <td>6.084022e-13</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>394</td>\n",
       "      <td>215</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1000 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Fx            Fy            Fz      Mach            Mx  \\\n",
       "time                                                                      \n",
       "0.01   1.682565e-11  3.988299e-17  2.364686e-11  0.133756  2.931208e-14   \n",
       "0.02   1.682565e-11  1.113008e-16  2.364686e-11  0.133756  2.830690e-14   \n",
       "0.03   1.682565e-11  2.118543e-16  2.364686e-11  0.133756  2.734757e-14   \n",
       "0.04   1.682565e-11  3.406791e-16  2.364686e-11  0.133756  2.643204e-14   \n",
       "0.05   1.682565e-11  4.969478e-16  2.364686e-11  0.133756  2.555839e-14   \n",
       "0.06   1.671197e-11  6.798681e-16  2.546585e-11  0.133756  2.472474e-14   \n",
       "0.07   1.671197e-11  8.886811e-16  2.546585e-11  0.133756  2.392932e-14   \n",
       "0.08   1.671197e-11  1.122661e-15  2.546585e-11  0.133756  2.317044e-14   \n",
       "0.09   1.671197e-11  1.381110e-15  2.546585e-11  0.133756  2.244646e-14   \n",
       "0.10   1.682565e-11  1.663364e-15  2.546585e-11  0.133756  2.175583e-14   \n",
       "0.11   1.705303e-11  1.968783e-15  2.546585e-11  0.133756  2.109706e-14   \n",
       "0.12   1.716671e-11  2.296755e-15  2.546585e-11  0.133756  2.046872e-14   \n",
       "0.13   1.728040e-11  2.646694e-15  2.546585e-11  0.133756  1.986945e-14   \n",
       "0.14   1.739409e-11  3.018038e-15  2.546585e-11  0.133756  1.929794e-14   \n",
       "0.15   1.750777e-11  3.410248e-15  2.546585e-11  0.133756  1.875295e-14   \n",
       "0.16   1.762146e-11  3.816426e-15  2.728484e-11  0.133756  1.819868e-14   \n",
       "0.17   1.773515e-11  4.196172e-15  2.728484e-11  0.133756  1.744420e-14   \n",
       "0.18   1.750777e-11  4.585643e-15  2.910383e-11  0.133756  1.670343e-14   \n",
       "0.19   1.762146e-11  5.007389e-15  2.910383e-11  0.133756  1.609528e-14   \n",
       "0.20   1.784883e-11  5.449073e-15  2.910383e-11  0.133756  1.554361e-14   \n",
       "0.21   1.784883e-11  5.904860e-15  2.910383e-11  0.133756  1.501568e-14   \n",
       "0.22   1.750777e-11  6.378532e-15  3.456080e-11  0.133756  1.453281e-14   \n",
       "0.23   1.750777e-11  6.868901e-15  3.456080e-11  0.133756  1.408436e-14   \n",
       "0.24   1.750777e-11  7.388058e-15  3.637979e-11  0.133756  1.373220e-14   \n",
       "0.25   1.762146e-11  7.912658e-15  3.819878e-11  0.133756  1.334583e-14   \n",
       "0.26   1.762146e-11  8.435388e-15  4.001777e-11  0.133756  1.290080e-14   \n",
       "0.27   1.773515e-11  8.990677e-15  4.001777e-11  0.133756  1.258186e-14   \n",
       "0.28   1.750777e-11  9.568884e-15  4.183676e-11  0.133756  1.232674e-14   \n",
       "0.29   1.762146e-11  1.017752e-14  4.365575e-11  0.133756  1.216324e-14   \n",
       "0.30   1.762146e-11  1.077698e-14  4.365575e-11  0.133756  1.188180e-14   \n",
       "...             ...           ...           ...       ...           ...   \n",
       "9.71   1.496119e-10  9.333875e-13  6.366463e-11  0.133756  2.985816e-16   \n",
       "9.72   1.497256e-10  9.345363e-13  6.366463e-11  0.133756  3.020084e-16   \n",
       "9.73   1.498393e-10  9.356856e-13  6.366463e-11  0.133756  3.054401e-16   \n",
       "9.74   1.500666e-10  9.368356e-13  6.366463e-11  0.133756  3.088762e-16   \n",
       "9.75   1.501803e-10  9.379861e-13  6.366463e-11  0.133756  3.123162e-16   \n",
       "9.76   1.502940e-10  9.391371e-13  6.366463e-11  0.133756  3.157596e-16   \n",
       "9.77   1.504077e-10  9.402888e-13  6.548362e-11  0.133756  3.192060e-16   \n",
       "9.78   1.505214e-10  9.414411e-13  6.548362e-11  0.133756  3.226548e-16   \n",
       "9.79   1.505214e-10  9.425939e-13  6.548362e-11  0.133756  3.261057e-16   \n",
       "9.80   1.507487e-10  9.437473e-13  6.548362e-11  0.133756  3.295581e-16   \n",
       "9.81   1.508624e-10  9.449014e-13  6.548362e-11  0.133756  3.330116e-16   \n",
       "9.82   1.509761e-10  9.460560e-13  6.548362e-11  0.133756  3.364657e-16   \n",
       "9.83   1.510898e-10  9.472112e-13  6.548362e-11  0.133756  3.399199e-16   \n",
       "9.84   1.513172e-10  9.483671e-13  6.548362e-11  0.133756  3.433738e-16   \n",
       "9.85   1.514309e-10  9.495235e-13  6.548362e-11  0.133756  3.468269e-16   \n",
       "9.86   1.515446e-10  9.506806e-13  6.548362e-11  0.133756  3.502788e-16   \n",
       "9.87   1.516582e-10  9.518383e-13  6.548362e-11  0.133756  3.537290e-16   \n",
       "9.88   1.517719e-10  9.529966e-13  6.548362e-11  0.133756  3.571770e-16   \n",
       "9.89   1.521130e-10  9.541555e-13  6.548362e-11  0.133756  3.606225e-16   \n",
       "9.90   1.522267e-10  9.553150e-13  6.548362e-11  0.133756  3.640649e-16   \n",
       "9.91   1.523404e-10  9.564752e-13  6.548362e-11  0.133756  3.675038e-16   \n",
       "9.92   1.524540e-10  9.576360e-13  6.548362e-11  0.133756  3.709388e-16   \n",
       "9.93   1.526814e-10  9.587975e-13  6.548362e-11  0.133756  3.743695e-16   \n",
       "9.94   1.527951e-10  9.599596e-13  6.548362e-11  0.133756  3.777954e-16   \n",
       "9.95   1.529088e-10  9.611223e-13  6.548362e-11  0.133756  3.812161e-16   \n",
       "9.96   1.530225e-10  9.622857e-13  6.548362e-11  0.133756  3.846312e-16   \n",
       "9.97   1.531362e-10  9.634497e-13  6.548362e-11  0.133756  3.880402e-16   \n",
       "9.98   1.533635e-10  9.646144e-13  6.548362e-11  0.133756  3.914427e-16   \n",
       "9.99   1.534772e-10  9.657797e-13  6.548362e-11  0.133756  3.948383e-16   \n",
       "10.00  1.535909e-10  9.669457e-13  6.548362e-11  0.133756  3.982266e-16   \n",
       "\n",
       "                 My            Mz   TAS           a       aileron   ...     \\\n",
       "time                                                                ...      \n",
       "0.01  -1.502423e-11  3.036133e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.02  -1.456759e-11  3.008343e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.03  -1.412482e-11  2.981037e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.04  -1.369551e-11  2.954186e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.05  -1.327925e-11  2.927764e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.06  -1.287564e-11  2.901745e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.07  -1.248430e-11  2.876107e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.08  -1.210485e-11  2.850826e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.09  -1.173694e-11  2.825879e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.10  -1.138021e-11  2.801248e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.11  -1.103432e-11  2.776911e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.12  -1.069894e-11  2.752851e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.13  -1.037376e-11  2.729050e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.14  -1.005846e-11  2.705491e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.15  -9.752741e-12  2.682158e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.16  -9.079912e-12 -7.014492e-16  45.0  336.434581  2.492525e-18   ...      \n",
       "0.17  -8.803938e-12 -8.500321e-16  45.0  336.434581  2.492525e-18   ...      \n",
       "0.18  -8.156199e-12  8.450127e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.19  -7.147997e-12  1.098344e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.20  -6.930741e-12  1.081493e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.21  -6.720088e-12  1.064987e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.22  -6.143234e-12  1.553733e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.23  -5.576365e-12  2.210854e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.24  -5.406877e-12  2.191748e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.25  -4.869937e-12  1.028275e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.26  -4.341769e-12  1.957141e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.27  -4.209805e-12  1.939235e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.28  -3.709249e-12  3.032277e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.29  -3.216358e-12  1.797171e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.30  -2.738449e-12  1.206311e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "...             ...           ...   ...         ...           ...   ...      \n",
       "9.71   3.356707e-26  7.112137e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.72   3.222438e-26  7.119961e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.73   3.088170e-26  7.127691e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.74   3.088170e-26  7.135326e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.75   2.953902e-26  7.142868e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.76   2.819634e-26  7.150315e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.77   2.551097e-26  7.157668e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.78   2.551097e-26  7.164927e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.79   2.416829e-26  7.172090e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.80   2.282561e-26  7.179160e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.81   2.148292e-26  7.186134e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.82   2.014024e-26  7.193015e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.83   2.014024e-26  7.199800e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.84   1.879756e-26  7.206491e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.85   1.745487e-26  7.213087e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.86   1.745487e-26  7.219589e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.87   1.745487e-26  7.225996e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.88   1.745487e-26  7.232309e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.89   1.745487e-26  7.238527e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.90   1.745487e-26  7.244651e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.91   1.745487e-26  7.250681e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.92   1.745487e-26  7.256617e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.93   1.745487e-26  7.262459e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.94   1.745487e-26  7.268207e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.95   1.745487e-26  7.273862e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.96   1.745487e-26  7.279423e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.97   1.745487e-26  7.284891e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.98   1.745487e-26  7.290265e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "9.99   1.745487e-26  7.295547e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "10.00  1.745487e-26  7.300736e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "\n",
       "         thrust         u             v        v_down     v_east    v_north  \\\n",
       "time                                                                          \n",
       "0.01   0.577997  44.87164  8.373417e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.02   0.577997  44.87164  8.372773e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.03   0.577997  44.87164  8.371706e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.04   0.577997  44.87164  8.370221e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.05   0.577997  44.87164  8.368322e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.06   0.577997  44.87164  8.366015e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.07   0.577997  44.87164  8.363303e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.08   0.577997  44.87164  8.360192e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.09   0.577997  44.87164  8.356686e-16  4.440892e-16  21.574149  39.491215   \n",
       "0.10   0.577997  44.87164  8.352790e-16  8.881784e-16  21.574149  39.491215   \n",
       "0.11   0.577997  44.87164  8.348508e-16  1.776357e-15  21.574149  39.491215   \n",
       "0.12   0.577997  44.87164  8.343846e-16  2.220446e-15  21.574149  39.491215   \n",
       "0.13   0.577997  44.87164  8.338806e-16  2.664535e-15  21.574149  39.491215   \n",
       "0.14   0.577997  44.87164  8.333395e-16  3.552714e-15  21.574149  39.491215   \n",
       "0.15   0.577997  44.87164  8.327615e-16  3.996803e-15  21.574149  39.491215   \n",
       "0.16   0.577997  44.87164  8.321473e-16  4.440892e-15  21.574149  39.491215   \n",
       "0.17   0.577997  44.87164  8.315258e-16  4.440892e-15  21.574149  39.491215   \n",
       "0.18   0.577997  44.87164  8.309147e-16  4.440892e-15  21.574149  39.491215   \n",
       "0.19   0.577997  44.87164  8.303082e-16  4.884981e-15  21.574149  39.491215   \n",
       "0.20   0.577997  44.87164  8.296945e-16  4.884981e-15  21.574149  39.491215   \n",
       "0.21   0.577997  44.87164  8.290711e-16  5.329071e-15  21.574149  39.491215   \n",
       "0.22   0.577997  44.87164  8.284374e-16  5.329071e-15  21.574149  39.491215   \n",
       "0.23   0.577997  44.87164  8.277876e-16  5.329071e-15  21.574149  39.491215   \n",
       "0.24   0.577997  44.87164  8.271166e-16  5.773160e-15  21.574149  39.491215   \n",
       "0.25   0.577997  44.87164  8.264191e-16  5.773160e-15  21.574149  39.491215   \n",
       "0.26   0.577997  44.87164  8.257109e-16  6.217249e-15  21.574149  39.491215   \n",
       "0.27   0.577997  44.87164  8.249888e-16  6.217249e-15  21.574149  39.491215   \n",
       "0.28   0.577997  44.87164  8.242409e-16  6.217249e-15  21.574149  39.491215   \n",
       "0.29   0.577997  44.87164  8.234528e-16  6.661338e-15  21.574149  39.491215   \n",
       "0.30   0.577997  44.87164  8.226298e-16  6.661338e-15  21.574149  39.491215   \n",
       "...         ...       ...           ...           ...        ...        ...   \n",
       "9.71   0.577997  44.87164  1.049488e-15  5.906386e-13  21.574149  39.491215   \n",
       "9.72   0.577997  44.87164  1.050029e-15  5.910827e-13  21.574149  39.491215   \n",
       "9.73   0.577997  44.87164  1.050570e-15  5.919709e-13  21.574149  39.491215   \n",
       "9.74   0.577997  44.87164  1.051109e-15  5.924150e-13  21.574149  39.491215   \n",
       "9.75   0.577997  44.87164  1.051648e-15  5.933032e-13  21.574149  39.491215   \n",
       "9.76   0.577997  44.87164  1.052185e-15  5.937473e-13  21.574149  39.491215   \n",
       "9.77   0.577997  44.87164  1.052722e-15  5.946355e-13  21.574149  39.491215   \n",
       "9.78   0.577997  44.87164  1.053258e-15  5.955236e-13  21.574149  39.491215   \n",
       "9.79   0.577997  44.87164  1.053792e-15  5.955236e-13  21.574149  39.491215   \n",
       "9.80   0.577997  44.87164  1.054326e-15  5.959677e-13  21.574149  39.491215   \n",
       "9.81   0.577997  44.87164  1.054859e-15  5.968559e-13  21.574149  39.491215   \n",
       "9.82   0.577997  44.87164  1.055391e-15  5.973000e-13  21.574149  39.491215   \n",
       "9.83   0.577997  44.87164  1.055922e-15  5.977441e-13  21.574149  39.491215   \n",
       "9.84   0.577997  44.87164  1.056453e-15  5.986323e-13  21.574149  39.491215   \n",
       "9.85   0.577997  44.87164  1.056982e-15  5.990763e-13  21.574149  39.491215   \n",
       "9.86   0.577997  44.87164  1.057510e-15  5.999645e-13  21.574149  39.491215   \n",
       "9.87   0.577997  44.87164  1.058037e-15  6.004086e-13  21.574149  39.491215   \n",
       "9.88   0.577997  44.87164  1.058563e-15  6.008527e-13  21.574149  39.491215   \n",
       "9.89   0.577997  44.87164  1.059089e-15  6.017409e-13  21.574149  39.491215   \n",
       "9.90   0.577997  44.87164  1.059613e-15  6.021850e-13  21.574149  39.491215   \n",
       "9.91   0.577997  44.87164  1.060137e-15  6.030731e-13  21.574149  39.491215   \n",
       "9.92   0.577997  44.87164  1.060659e-15  6.035172e-13  21.574149  39.491215   \n",
       "9.93   0.577997  44.87164  1.061180e-15  6.039613e-13  21.574149  39.491215   \n",
       "9.94   0.577997  44.87164  1.061701e-15  6.048495e-13  21.574149  39.491215   \n",
       "9.95   0.577997  44.87164  1.062220e-15  6.052936e-13  21.574149  39.491215   \n",
       "9.96   0.577997  44.87164  1.062739e-15  6.061818e-13  21.574149  39.491215   \n",
       "9.97   0.577997  44.87164  1.063256e-15  6.066259e-13  21.574149  39.491215   \n",
       "9.98   0.577997  44.87164  1.063773e-15  6.070699e-13  21.574149  39.491215   \n",
       "9.99   0.577997  44.87164  1.064288e-15  6.079581e-13  21.574149  39.491215   \n",
       "10.00  0.577997  44.87164  1.064803e-15  6.084022e-13  21.574149  39.491215   \n",
       "\n",
       "              w  x_earth  y_earth  z_earth  \n",
       "time                                        \n",
       "0.01   3.396464        0        0    -1000  \n",
       "0.02   3.396464        0        0    -1000  \n",
       "0.03   3.396464        1        0    -1000  \n",
       "0.04   3.396464        1        0    -1000  \n",
       "0.05   3.396464        1        1    -1000  \n",
       "0.06   3.396464        2        1    -1000  \n",
       "0.07   3.396464        2        1    -1000  \n",
       "0.08   3.396464        3        1    -1000  \n",
       "0.09   3.396464        3        1    -1000  \n",
       "0.10   3.396464        3        2    -1000  \n",
       "0.11   3.396464        4        2    -1000  \n",
       "0.12   3.396464        4        2    -1000  \n",
       "0.13   3.396464        5        2    -1000  \n",
       "0.14   3.396464        5        3    -1000  \n",
       "0.15   3.396464        5        3    -1000  \n",
       "0.16   3.396464        6        3    -1000  \n",
       "0.17   3.396464        6        3    -1000  \n",
       "0.18   3.396464        7        3    -1000  \n",
       "0.19   3.396464        7        4    -1000  \n",
       "0.20   3.396464        7        4    -1000  \n",
       "0.21   3.396464        8        4    -1000  \n",
       "0.22   3.396464        8        4    -1000  \n",
       "0.23   3.396464        9        4    -1000  \n",
       "0.24   3.396464        9        5    -1000  \n",
       "0.25   3.396464        9        5    -1000  \n",
       "0.26   3.396464       10        5    -1000  \n",
       "0.27   3.396464       10        5    -1000  \n",
       "0.28   3.396464       11        6    -1000  \n",
       "0.29   3.396464       11        6    -1000  \n",
       "0.30   3.396464       11        6    -1000  \n",
       "...         ...      ...      ...      ...  \n",
       "9.71   3.396464      383      209    -1000  \n",
       "9.72   3.396464      383      209    -1000  \n",
       "9.73   3.396464      384      209    -1000  \n",
       "9.74   3.396464      384      210    -1000  \n",
       "9.75   3.396464      385      210    -1000  \n",
       "9.76   3.396464      385      210    -1000  \n",
       "9.77   3.396464      385      210    -1000  \n",
       "9.78   3.396464      386      210    -1000  \n",
       "9.79   3.396464      386      211    -1000  \n",
       "9.80   3.396464      387      211    -1000  \n",
       "9.81   3.396464      387      211    -1000  \n",
       "9.82   3.396464      387      211    -1000  \n",
       "9.83   3.396464      388      212    -1000  \n",
       "9.84   3.396464      388      212    -1000  \n",
       "9.85   3.396464      388      212    -1000  \n",
       "9.86   3.396464      389      212    -1000  \n",
       "9.87   3.396464      389      212    -1000  \n",
       "9.88   3.396464      390      213    -1000  \n",
       "9.89   3.396464      390      213    -1000  \n",
       "9.90   3.396464      390      213    -1000  \n",
       "9.91   3.396464      391      213    -1000  \n",
       "9.92   3.396464      391      214    -1000  \n",
       "9.93   3.396464      392      214    -1000  \n",
       "9.94   3.396464      392      214    -1000  \n",
       "9.95   3.396464      392      214    -1000  \n",
       "9.96   3.396464      393      214    -1000  \n",
       "9.97   3.396464      393      215    -1000  \n",
       "9.98   3.396464      394      215    -1000  \n",
       "9.99   3.396464      394      215    -1000  \n",
       "10.00  3.396464      394      215    -1000  \n",
       "\n",
       "[1000 rows x 35 columns]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "kwargs = {'marker': '.',\n",
    "          'subplots': True,\n",
    "          'sharex': True,\n",
    "          'figsize': (12, 6)}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
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YgDo4NMxL3cXfmJcbjnMD+uzGej7w+uXeLU+SqpjhWVLV2TscjwbUrt4BuvuG6O4f3rO2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\nsmpE1YVnSZJmvL0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7a1b81f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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aW5KkQzG6mMvmH06cXaPRgXrZCS7mItWQgVmSpJlQLlDXeqnxySw6BjoWjg3z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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb754b7c668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['psi', 'theta', 'phi'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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MMgxLkiQpswzDkiRJyizDsCRJkjLLMCxJkqTM+v9VfWTljwyz8wAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb754a311d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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0jW8PD9KuAQAAEAEE59mY0J4xSrsGAABABBCcZ6O/RxNm1HhjbWhDAQAAQGkQ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\nAkBwBoAiSw/JvYO9ga+yN7b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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7548805c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['p', 'q', 'r'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7548b9b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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MVP5Btvanw/L2+WHX1gZJUp0zGEvlVuyhNhJMTlS+t3flWdCy3NYGSZLmMBhL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\n9XDLD24BoPdQL+effn7GFUm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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb75467ec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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H0kWSTpR0uZmdmGa7uTPtNEkmTaiLhuaGq3LdIwAAAAQgreDs7q+6+/phDjtD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\nFvdmO1bSfklLJcm5aaMYLZJ0vKRT3P0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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb754589ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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mFi9ebOCuykwWL15Mc3PzZo/h3UgkSZIEQEtLC52dnXR1dZVdSr/R3NxMS0vL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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb754677a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Doublet "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's set the controls for the aircraft during the simulation. As a first step we will set them constant and equal to the trimmed values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pyfme.utils.input_generator import Doublet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "de0 = trimmed_controls['delta_elevator']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "controls = controls = {\n",
    "    'delta_elevator': Doublet(t_init=2, T=1, A=0.1, offset=de0),\n",
    "    'delta_aileron': Constant(trimmed_controls['delta_aileron']),\n",
    "    'delta_rudder': Constant(trimmed_controls['delta_rudder']),\n",
    "    'delta_t': Constant(trimmed_controls['delta_t'])\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim = Simulation(aircraft, system, environment, controls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the simulation is set, the propagation can be performed:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "time: 90.00000000000914it [00:48,  1.88it/s]                          \n"
     ]
    }
   ],
   "source": [
    "results = sim.propagate(90)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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Vh1roO955L/ja77OuQpKUIcOzpMr57lDY8EHWVRTWbyBc2pZ1FZKkKmZ4llQ+\n00bAmnezrqIwFwORJHWT4VlS6WphvmOXkpYk9SDDs6SP1ELf8aDh8P8szLoKSVKdMjxL9aba+45d\nDESSVMUMz1JvU+3zHYNLSUuSapbhWao1VT/fMbDfMXDOfVlXIUlS2RmepWp05e6QNmZdRWH2HUuS\n6pThWcpCtfcdO9+xJEkdMjxLPaHa5zsG+44lSeoCw7PUFf/cAivfzLqK4pzvWJKksjM8S4XYdyxJ\nkrZheFb9+s6esHFt1lUUFg3wrXeyrkKSJLVjeFbvdc0wWLcq6yqKs+9YkqSaYnhW7aqFpaSd71iS\npF7F8KzqNe8OePCirKsobsgBcOGzWVchSZIqxPCsbFX7RXl9GuGK5VlXIUmSqoThWT2r2hcDATj5\nemg9N+sqJElSDTA8q3tmToBXq3wu4ZYz4PSbs65CkiT1AoZnFffot+A/rsu6iuKaBsPU17OuQpIk\n1QHDc71b/CzcehywKetKCmvoD5e/nXUVkiRJhue6UO1LSbsYiCRJqhGG595g+jGwZH7WVRTnRXmS\nJKkXMDzXAvuOJUmSqoLhuVpU+3zHfQfAZUuzrkKSJClThudKqfa+YxcDkSRJ6pThuVxqYb5jl5KW\nJEnqloqH54g4HrgeaABuSSlNq3QNXTLvDnjwoqyrKG7nveBrv8+6CkmSpF6rouE5IhqAHwB/BbQB\ncyPigZTS7ypZR6euGQbrVmVdxfbsO5YkScpUpUeeDwVeSSm9ChAR9wCnAtUTnrMMzvYdS5IkVbVK\nh+d9gMXtbrcBh7XfISKmAFMAhg8fXrnKNuvp4GzfsSRJUs2qdHiODralrW6kNB2YDtDa2po62L9n\n9RvYvQDtfMeSJEm9VqXDcxuwb7vbw4AlFa6huEvbirdu2HcsSZJUtyodnucC+0fESOCPwJnApArX\n0LlL27KuQJIkSVUoUqpsZ0REnAhcR26quttSSlcX2XcZ8EalatvGcKCKVzVRhjw3VIjnhorx/FAh\nnhvV4eMppT0626ni4blWRMSyUn6Bqj+eGyrEc0PFeH6oEM+N2tIn6wKq2HtZF6Cq5bmhQjw3VIzn\nhwrx3KghhufCVmZdgKqW54YK8dxQMZ4fKsRzo4YYngubnnUBqlqeGyrEc0PFeH6oEM+NGmLPsyRJ\nklQiR54lSZKkEtV0eI6IiRHxQkRsiojWEvb/eETMj4gF+cd9uRJ1SpIkqXeomfAcEUdFxB3bbP4t\n8HngyRKfZilwREppDHAYMDUi9i5flZIkSerNaiY8dySltCil9NK22yOiISK+FxFzI+L5iLggv/+6\nlNLa/G79qfHXL0mSpMrqreEIOVvrAAAc+0lEQVTxfGBlSukQ4BDgS/klwYmIfSPieWAx8I8ppSUZ\n1ilJkqQa0jfrAjoTEc+QGyXeBdg9Ihbk7/pGSumRAg87FhgdEf8tf3sQsD/wWkppcf6+vYGfRcRP\nUkpv9eBLkCRJUi9R9eE5pXQY5HqegXNTSueW8LAAvlokXJNSWhIRLwB/AfykDKVKkiSpl+utbRuP\nAF+JiEaAiPhkROwcEcMiYqf8tsHAZ4DteqYlSZKkjlT9yHMxETEB+F/AHsBDEbEgpXQccAswAvh1\nRASwDDgNOBD4p4hI5Eanv59SWphJ8ZIkSao5rjAoSZIklai3tm1IkiRJZVfVbRtDhgxJI0aMyLoM\nSZIk9XLz589fnlLao7P9qjo8jxgxgnnz5mVdhiRJknq5iHijlP2qOjxL3XXcrONY8kHH6+Ds3LAz\nc86aU+GKJElSLTM8q9e4YPYFPL306ZL3X71xNS0zWrbaNqT/EB4/8/FylyZJknoJw7Nq3tgZY9nA\nhrI81/K1y7cE6r0H7M0jEwuusyNJkuqQ4Vk1acHbCzjn5+eQ6LmpFpd8sISWGS30i37MP2d+jx1H\nkqSetn79etra2lizZk3WpWSuqamJYcOG0djY2KXHG55Vc8o50lyKdWmdIVqSVNPa2toYOHAgI0aM\nILd+XH1KKbFixQra2toYOXJkl57DeZ5VMyY9OImWGS1dCs4tzS0snLyQhZMXct7B53Xp+JtD9NH3\nHN2lx0uSlJU1a9bQ3Nxc18EZICJobm7u1gi8I8+qCdte2FfMoMZBPDXpqYL3X9x6MRe3XrzVth25\n2HBzX/QRQ4/gX4/915LrkiQpS/UenDfr7u/B8Kyqdu28a7n9hds73S8IZp4wkzF7junScdqH4FPv\nO5VX//Rqp495eunTtMzIjWhLkqT6YNuGqtbR9xzdaXDuQx8WTl7I85Of73Jw3tb9E+5n4eSFXDH+\nipL2b5nRwgWzLyjLsSVJ6q1ef/11Ro0aVfL+N910EzNnziy6zx133MGFF17Y4X3XXHPNDtVXKsOz\nqtLYGWNZvnZ50X2uGH8Fv5n8mx6rYeIBE0sO0U8vfZrRM0b3WC2SJNWbL3/5y5xzzjldfrzhWXWj\ns4sCBzUOYuHkhUw8YGJF6tkcoo8YekTR/RKJlhktzHppVkXqkiSpJy14ewG3LLyFBW8vKNtzbty4\nkS996UscfPDBHHvssXz44Yf84Q9/4Pjjj2fcuHH8xV/8BS+++CIA3/72t/n+978PwNy5cxk9ejSH\nH344X/va17YawV6yZAnHH388+++/P1//+tcBmDp1Kh9++CFjxozhC1/4QtnqhzL2PEfE8cD1QANw\nS0pp2jb39wdmAuOAFcB/Tym9Xq7jq3fo7MLAK8ZfUbHQvK3NfdGH3HkIazYVvkr3qjlXccvzt7jA\niiSpKv3js//Ii++8WHSf99e9z0vvvkQiEQQHDD6AXfrtUnD/P9/9z/nGod/o9Ngvv/wyP/rRj7j5\n5ps544wz+OlPf8rtt9/OTTfdxP77788zzzzDX//1X/PYY49t9bjzzjuP6dOnc8QRRzB16tSt7luw\nYAHPPfcc/fv354ADDuCrX/0q06ZN48Ybb2TBgvIF/83KMvIcEQ3AD4ATgIOA/xERB22z2/nAuyml\nTwD/DPxjOY5dTcbfNZ6WGS18euany/oprV50FpwrOdpczNyz53bayrHkgyW2cUiSataq9au2LESW\nSKxav6oszzty5EjGjMldozRu3Dhef/11nn76aSZOnMiYMWO44IILWLp06VaPee+991i1ahVHHJH7\nBnjSpElb3f+5z32OQYMG0dTUxEEHHcQbb7xRlloLKdfI86HAKymlVwEi4h7gVOB37fY5Ffh2/uef\nADdGRKSUem6JuC465K5DWLOx6/P/rU/rOfvnZ3PnCXeW7SK23q5YcG6ggQWTq+vDyMQDJjLxgIlF\nR6E3t3E4G4ckqZqUMkK84O0FfGn2l1i/aT2NfRqZ9hfTypJp+vfvv+XnhoYG3nrrLXbbbbeiI8Sd\nRcVtn3PDhp5dSK1cPc/7AIvb3W7Lb+twn5TSBmAl0Fym45fN+LvGdys4t3f2z88uy/P0dsWC86DG\nQVUXnNube/bcThddaZnRwrXzrq1QRZIkdd+YPcdw87E3c+HYC7n52Jt7bDBw1113ZeTIkcyalbte\nKKXEb36z9WQAgwcPZuDAgcyZMweAe+65p6TnbmxsZP369eUtmPKF545mm972Y0Ip+xARUyJiXkTM\nW7ZsWVmK2xGrN64u6/MZmoorFpz323W/ooudVIuLWy/udHT59hdud2VCSVJNGbPnGL7Y8sUe/xb9\nhz/8Ibfeeiuf+tSnOPjgg7n//vu32+fWW29lypQpHH744aSUGDRoUKfPO2XKFEaPHl32CwajHF0T\nEXE48O2U0nH525cApJT+od0+j+T3+VVE9AX+E9ijWNtGa2trmjdvXrfr2xHj7xpf1gA9oGEAz5z1\nTNmerzcpFpxbmlu4++S7K1hNeXR2MWEf+vTo9HqSJHVk0aJFHHjggVmX0WXvv/8+u+ySu2Bx2rRp\nLF26lOuvv77Lz9fR7yMi5qeUWjt7bLlGnucC+0fEyIjoB5wJPLDNPg8Ak/M//zfgsWrsd55z1hx2\nbti5bM9XrhaQ3mbsjLEF79tv1/1qMjhDro3jpJEnFbx/E5t2aKlxSZIEDz30EGPGjGHUqFH8+7//\nO5dddllmtZRl5BkgIk4EriM3Vd1tKaWrI+IqYF5K6YGIaALuBMYC7wBnbr7AsJAsRp67a8yMMWxk\n45bbjX0a+fXZv86wourz2bs/y8r1Kzu8b+8Be/eaKd5KmT1EkqRKqPWR53Lrzshz2eZ5Tik9DDy8\nzbYr2v28Bsh+nrEe1tS3idUbPmr7iA5bvevXpAcnFQzOQ/oP6TXBGXLhuGhryowWzjv4PC5uvbiC\nVamSFry9oEcvHO5NHzYl9byUEhHmku4OHJctPCunX0O/rcLzuk3rmPXSrKqYnzhrs16axcIVHY+2\nNvVp4vEzH69wRT1v4eSFjJs5jnVpXYf33/7C7Tzy2iMGoF6gp4NyR5Z8sKTDD2hZLiYkqTo1NTWx\nYsUKmpub6zpAp5RYsWIFTU1NXX6OsrVt9IRabNu4dt613P7C7Vtt22/Qftx/2vZXjtabQqOw9XAR\n3XGzjmPJB0sK3t/Up4m5Z8+tYEUqh2IfjKrJkP5DeuWHU0mlW79+PW1tbaxZ47VYTU1NDBs2jMbG\nxq22l9q2YXjuAYf98DA+2PDBltt777w3j/y3+h5ZLNa+UC+9vx19sGqvHj5E9AbbXtdQi2z3kKTt\nVXq2DbWz78B9t7o9sN/AjCqpDofceUjB++olOEPn80E7E0f1GjdzHC0zWmiZ0VLzwRk+avdomdHC\n6BmjmfXSrKxLkqSaYc9zD1i/aX3R2/XkgtkXFJz3+M4T7qxwNdWhlAsJ6+lDRbU69b5TefVPRScE\nKllf+vLc5OfK8lxQ3toSiavmXMVVc64CclNF3j/BNjNJKsTw3AMa+zQWvV0vFry9gKeXPt3hfUcM\nPaLHVyyqZqUEaC/6ykZ3+5jLHZQ7UijclqMH+9U/vbrl3OwX/Zh/zvxuPZ+qRxYXtXbkpJEnMe3I\naVmXIXWZPc894NSfncqrKz8aFarXCwYLhcOdG3ZmzllzKlxNdRo7Yywb2FDw/lpdabHWzHpp1paR\n166o1g86kx6cVHCGm66o1tepzi9KrlVeTK1K8oLBDJ3783OZ//ZHozXj9hzHHSfckV1BGSgWCm1J\n2NrR9xzN8rXLC97vh42eM/XJqTz02kM7/LhKjC73hHK2e/jBrvJ6a0AuB9uNqldnF8t3pIEGFkxe\n0EMVFWZ4zlC9h+dio10G5451FuKC4PnJz1ewot7tgtkXFGwpKqa3jbyWa6o9RwfLy5DcM4Jg5gkz\n67plcEd1dYChHLII0BVfYVAfeXftu1vdXrp6aUaVVN6CtxcUDM5XjL+iw+2CaUdO48w/P7NgP2Ii\neSFhGXRl5LU3T+vWvp+5O4FtzaY1W7VpHTH0CP712H/tdn29XXfbhbRjEmmHer57y7crnX27Wa2q\neWYjR557wEWPXcRjix/bcruePu0W6nPuzQGk3Dqbrq63jX5WQld6f+v591zOUFdP73/FVNNoclYX\ngn727s+ycv3Kih9XtamaR54Nzz2goyuaz/jkGVx++OUZVVQZ4+8az+qNq7fb7uIfO66zAO2HkdLs\naGh2domOlXMlxSC4fPzlvfaDSdajyb2l97crfbLqPex57oZaDc8Akx6axMLlH/2jfcy+x3D9Mddn\nWFHPKtYXZatB1xxy5yEF58gGP5QUs6M9zV6UWbqeGEGt1d9/Z7Pl9JTeEpDLoZpG9FVcLVwbYc9z\nxnbvv3vWJVRUoeB83sHnVbiS3mPu2XOL9uhuXpHQDycf2dGLW4b0H8LjZz7egxX1Pu2/8SjX6ODq\njas7/LalGnpOC32jVgmG5M6V+g1cVh90eota/YDbUxx57iHb9j335pHnMTPGdNjYP6hxEE9NeiqD\ninqXUr4GrvcLtHY0xNn20jOy6GntasDOMhRvqxZG5OpJrV5g15lq+DBa7WzbyFi9hOdiX487Ilpe\nnfVB1+N0djvaX2porixH+7ZngJGql20bqohCwfnOE+6scCW938LJC4uGkc3T2Z138Hlc3Hpxhaur\nrB0NzbZnZGPbhWTKeeFhtfPiU6n3Mjyry0bPGN3h9pbmlrqflqqnPDf5uU4vhrv9hdu584U7a3IF\nvM50NJNNMbYOVZdtw2SWCzCUi1PxSfXH8KwuOW7WcSS2b/lpoMGvJHvY5t7mYm0cG9hAy4yWXtML\nvaM9zV7cUhumHTmNaUdO2257Nfac1sM3OpJKY3jWDpv10qyCUwNlMS9jvVo4eWGn09k9vfTpmp6R\nY0dHJr3wqncopcWmXAH7pJEndRjgJakQw7N2WKFe05NGnlThSjT37Lkljcq2zGipqdHYHZ271dBc\nf+xhl5QVw7N2yNH3HN3h9qY+TY7eZOTi1ou5uPXiglMGbrZ5Lt1qDtE7ekGZF2VJkirN8KySzXpp\nVsGvSR31y96CyQtKGoXeHKKrJXju6BLaYGiWJGWn2+E5InYHfgyMAF4HzkgpvdvBfhuBzf9CvplS\nOqW7x1ZlFWrXcBXB6rF5FLqUxSrWpXVbLjqs9IWFXV2ZzvYMSVLWyjHyPBX4ZUppWkRMzd/+Rgf7\nfZhSqtu5fFaureyqW+U2/q7xHW7fuWFnr0CvQpunZ+tsYZXNNl9YCD13AdWO9jG3V82tJpKk+lKO\n8HwqcFT+5xnAE3QcnutK807NW91+7u3nWPD2gpqcC/TaedcWXMbWQFPdFk5euMOjvA+99tBWM1x0\ndYquzmYCKcV+u+7H/RPu79ZzSJJUTt1enjsi3ksp7dbu9rsppcEd7LcBWABsAKallH5W4PmmAFMA\nhg8fPu6NN97oVn1ZWfD2As75+TlbzYV8xifP4PLDL8+wqq4pNHrpvKe1pVYWpAiCy8dfzsQDJmZd\niiSpjpR1ee6I+AXwsQ7u+uYO1DQ8pbQkIvYDHouIhSmlP2y7U0ppOjAdoLW1tXvJPkNj9hzDp4Z8\nigXLP5r3ePmH1TXpfynGzRzX4fZBjYMMzjVm84IUO7q0daW4hLYkqRaUFJ5TSn9Z6L6IeCsihqaU\nlkbEUODtAs+xJP/3qxHxBDAW2C489ya777R71iV0y9QnpxacNswlj2vXxAMmbhnVLeXCwp5kL7Mk\nqdaUo+f5AWAyMC3/93YNihExGPggpbQ2IoYAnwH+vzIcWz2o0Ff8d55wZ4UrUU9p/yFo/F3jC/a2\nl5N9zJKkWlaO8DwNuDcizgfeBCYCREQr8OWU0heBA4F/jYhNQB9yPc+/K8Ox1UPGzOj4wsb9dt2v\nJi96VOe2HQEuV5i2N16S1Jt0OzynlFYAn+tg+zzgi/mfnwZKmzNLmTv1vlM7XKkuCEcM64jtFJIk\nba9P1gWousx6aRav/unVDu97fvLzFa5GkiSpuhietZVCszAcMfSIClciSZJUfQzP2qLQKoJ96VvR\npZslSZKqleFZQPFVBJ+b/FyFq5EkSapOhmcBFFy++byDz6twJZIkSdXL8Cw+NeNTHW53FUFJkqSt\nGZ4raOXa7FZyK+Toe45mE5s6vM9VBCVJkrZmeO5BzTs1b3X7ubefY8HbCzKqZnvXzruW5WuXd3if\nqwhKkiRtz/Dcg075s1MIYsvtTWzi3/7wbxlWtLVCfc4tzS2uIihJktQBw3MPGrPnGD4x6BNbbfvD\ne3/IqJqttczoeMHHftGPu0++u8LVSJIk1QbDcw/bdpnrd9e+m1ElHxk3c1zB++afM7+ClUiSJNUW\nw3MPG9x/cNHblXbcrONYl9Z1eN/CyQsrXI0kSVJtMTz3sEH9BxW9XUlTn5zKkg+WdHjfSSNPqnA1\nkiRJtcfwXCcWvL2Ah157qMP7dm7YmWlHTqtwRZIkSbXH8Fwnzv752R1u70Mf5pw1p8LVSJIk1SbD\ncw/bdmGULBZKKTSzBsBvJv+mgpVIkiTVNsNzD9t2do1Kz7ZRLDh7gaAkSdKOMTz3sMY+jUVv96Ri\nwdkVBCVJknac4bmHrd+0fqvbKz5cUZHjFgvOJ408yRUEJUmSusDw3MNG7Dpiq9vL1yxn1kuzevSY\nxYLzfrvu58wakiRJXWR47mHnjTpvu213Lbqrx45XLDjvPWBv7p9wf48dW5IkqbczPPewMXuOYUjT\nkK22rdmwpuzHuWD2BZ0G50cmPlL240qSJNWTbofniJgYES9ExKaIaC2y3/ER8VJEvBIRU7t73FrS\nvFPzVrcH9htY1uf/1IxP8fTSpwveb3CWJEkqj3KMPP8W+DzwZKEdIqIB+AFwAnAQ8D8i4qAyHLsm\nbHuRYLkuGtw82ryJTQX3aWluMThLkiSVSd/uPkFKaRFARBTb7VDglZTSq/l97wFOBX7X3ePXgg/W\nf7DV7VXrVgG58Nt+xPikkSeVdDHfto8r5IrxVzDxgIk7WK0kSZIK6XZ4LtE+wOJ2t9uAwyp07Mxt\n+8Fi7aa1jJ4xmkTaavtDrz3EQ689xM4NO3e4ZPaYGWPYyMaSjukCKJIkSeVXUniOiF8AH+vgrm+m\nlEqZvqGjYenUwTYiYgowBWD48OGllFf1+jX0Y/WG1Vtt2zY4t7d64+qiF/8V05e+PDf5uS49VpIk\nScWV1POcUvrLlNKoDv6UOu9ZG7Bvu9vDgCUFjjU9pdSaUmrdY489Snz66nbaJ06ryHFOGnmSwVmS\nJKkHVaptYy6wf0SMBP4InAlMqtCxM3dx68Xc/sLtPfb8Q/oP4fEzH++x55ckSVJOt8NzREwA/hew\nB/BQRCxIKR0XEXsDt6SUTkwpbYiIC4FHgAbgtpTSC909di3pG33ZkDaU9TkHNQ7iqUlPlfU5JUmS\nVFg5Ztu4D7ivg+1LgBPb3X4YeLi7x6tVZx90doejz+3nYJ765FQeeu2hos9jT7MkSVJ2IqXCF65l\nrbW1Nc2bNy/rMsrm2nnXbhWgS52aTpIkST0rIuanlAou+LdlP8OzJEmS6l2vCM8RsQx4I6PDDwfe\nzOjYqm6eGyrEc0PFeH6oEM+N6vDxlFKnU71VdXjOUkQsK+UXqPrjuaFCPDdUjOeHCvHcqC0lzfNc\np97LugBVLc8NFeK5oWI8P1SI50YNMTwXtjLrAlS1PDdUiOeGivH8UCGeGzXE8FzY9KwLUNXy3FAh\nnhsqxvNDhXhu1BB7niVJkqQSOfIsSZIklcjwLEmSJJWorsNzRHR7eXJJkiTVj7oMzxHRNyK+D/xT\nRPxl1vWoukTEORHxXyJiUP52Xf5/ou1FxOkRMSYiGvK3I+uaVB1831Axvnf0LnV3wWD+hP0BMAh4\nGDgX+BlwS0ppbYalKUP58+JjwN3AJuAVYCDwtyml5RERqd7+ZxGw5dwYDvwE+BOwAngJ+KeU0nue\nG/UtIj4G3ANsxPcNteN7R+9Vj5+MBwJjgC+nlH4IfB/4JDAx06qUmYhoyL+BDQT+mFL6HPA3wHLg\nXzMtTpmKiF3z58Y+wNz8uXE5uXPl6kyLU6YiYu+IGELuXGjzfUPtRcQu+feOvYFnfO/oXeouPKeU\n/gS8Tm7EGeA/gOeAw/MjCKoT+fada4BrIuK/AAeQGz0ipbQBuAg4IiL+S0op+TVsfYmIvwGejIiD\ngGHA0PxdfwCuBT4bEYfkzw2/gq0TEdEn/74xBxhFbjAG8H1DW/27cl9EnAWcCuyav9v3jl6iXv+n\nvg8YExFDU0rvAwuBdXz0j6N6uXxYng8MJvdV63eA9cDREXEoQH7U4Crg2/nbmzIpVhXV7h+zgcAa\nYArwU6A1IsamlDaklN4E7iA30ohfvda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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7545f1cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['x_earth', 'y_earth', 'height'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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gSpIkSVVqu55pSZIkqVW01Q2IkyZNyp6enmaXIUmSpFFs2bJlz2Tm5EratlWY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\nX2liaWqi4nWxD3At8BqwCpg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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb75408ec50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['psi', 'theta', 'phi'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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PLeam+UuTnpcrAwuzJZ1ErNB/J7ns3FsXMH/J6rDDCJUGaYsUjqwPQPRIFr4hulkW/WoF\ntrj7m9H984BLgZ2S6WKwpUt/RGtb7s4xnci4kYOY+ImKmH8k6xubqVu+VrdCM+ignzzOpiTz3RVL\nz3B7UpzqhwuILDJUOW0uA/uWUn/5SVmMTo64ah5NXQdZF7mmDVtj3s3L1zuTha5Qr+FeBvdPVZtS\nUHrUM21mJURaOfYHbgSmAcuAM9y91syuB45z96oYj20B6oEWYIa7PxznNS4ALgAYMWLEuOXLl6cd\nbzruXrAi5qwW6ehdYp3m4M03Y372BBu2tsY8pv7pzIjXUtPR1In7Fu0A0HT6qvP9310u6e6UjJmQ\nyQ+Oid7DwlJiaP7+DEp3+k2JrdiLEllv8+jyYgOBh4CLgP7A/xLppX4KOMXdd2osM7Nh7r7SzPYF\nnibSGrLz9BcdBN3mkclEGgqjx27UtLnEumIM+LcS6rSlcntcSWFn6fzRLOYPIukIom0jFxfmyZWE\nTNXsCLUPFaZ8uMMaaDIdfcHLgY3ufk2HfScC33L3ryR57O3An919TqLzgk6mz7l1AX/P4D/gQqne\nxque6o0/PftdOpdkf7eVBMaXTrVRfa3xpbOqZioKZeGdXKpu5/t7birvfSIQXoU8iAGIQ4Bt7r7O\nzPoSqUL/Aljo7qvMrA/wGPBzd3+6y2MHAR+7+xYzqwBeBL7s7q8les18rkwX0q2SRL8XDUjsnlTa\nOgrlQ1i2pduCUGgzoXRXNnpGC+n9LlWn3vAc9Y3NYYeRUDZmYOrOeAaRngjjfSWIZPpQ4A6ghMgU\nt/e5+5Vm9kvgC9F9s9x9ZvT8GmCqu3/LzI4Cfge0Rc+bGWvGj67CmM0jEwl1If5hSTTLQrEnJ6lI\nZe5ofTBJT7q3hItlqsfurKKZKl2r8SnZzA+FdA1n6+5SLgi6uBR4m0cQ8m1qvEKXqK9Q1dT4Upmt\nQ7+/nuvJCnqF9AE4GysJavrBzFCbQ3ZowZ2ey8U+9YKsTIdByXTuSdSmoIRwZ8naOjSyPztS+QAT\nT74N/Mz0wGkorA8X+UDV7Nh0HRaGuuVrOXPWCzEnM4inYHumw6BkOjcpoU4ulQSnkG4z5qpMVFty\nbfBiNnqe9aEut2WjVScsutYklymZlkDFS6j1RpnawLgHdEsycJmc/iyo2Vay2QuZi1PUSWYEUeku\nljEHUlyUTEugEr1Z59tt8kyKNy93R6rehyvbiUaqtyez0Z6RSL5PqyYikm1KpiVwiSqwxfiHO1l/\ntPr/ck8uDrrJlHxYIEFEJJcomZZQJFrQINd6TbMllYRMi7DkvqArxZlWzHeEREQyQcm0hCZRX2eh\nT6mVylRXauvIT7m+KIcGsIqIZJaSaQlVol7hQk2ok7V1qFJYeHoy5V66NIeuiEgwlExL6BIll4XU\n8pFKW8ep1cOYOXlsQBFJLkh3+jJ96BIRyQ1KpiUnJEqoC2FQ4r7T5pKsLqm2DhERkfyTajLdK4hg\npHglSiQ3bG1l/8sSt0bkqrsXrKAySSJdYkqkRURECp2Sacm6RAllS1vyXuNcM+ZnT6S0mmGxL1Yj\nIiJSDJRMSyCSVWjzIaFur0bHm/qv3QPfOUqzKoiIiBQJJdMSmFQS6ovveTmgaLrngP96LGk1uneJ\nsWzGKZplQUREpIgomZZALZtxSsKL7uH6lTnVR33qDc9ROW0uW5NMHn1q9TDNwCAiIlKENJuHhCLR\nSontwpxObsZji7lp/tKUztUgQxERkcKj2Twkpy268mROrR6W8JyH61cG3kvd3hedSiI98RMVSqRF\nRESKnCrTErpUEua+pb1YfNXnshZDKguvtDPg30qiRURECpoWbZG8st+lc0nSlgxkfinlVNpNOtJK\nhiIiIsUhkGTazMqB+UAfoBSY4+6Xm9lxwDVAb6AO+Ka7t8R5jt2AxcBD7v69RK+nZLqwdXf55V4G\n90/tfmK9/2VzaUm2bGEXwweW89y047v3IBEREclbQSXTBuzq7hvMrAx4Dvg+cC9wvLu/aWZXAsvd\n/dY4z3E9MAT4UMm0ABz0k8fZ1N1st4PSXnDvt4/ijFkv9DiWbLeXiIiISG4KZACiR2yIbpZFv1qB\nLe7+ZnT/POCMOEGOA/YEnupJHFJYFl/1OR74zlFpP76ljR4n0n1Le7FsxilKpEVERCShHs/mYWYl\nZlYPrCKSOC8EysysPZM/E9gnxuN6AdcCP07y/BeYWa2Z1TY1NfU0XMkT40YOYtmMU7j6tKpAX3dg\n31Il0SIiIpKy0p4+gbu3AtVmNhB4CDgEmAxcZ2Z9iFSdY/VLXwg85u7vRLpF4j7/bGA2RNo8ehqv\n5JezJozgrAkjgPR6nVOlgYUiIiKSjh4n0+3cfZ2ZPQuc7O7XAMcAmNmJwAExHvJJ4BgzuxDoB/Q2\nsw3uPi1TMUlheevqHdPR9TSxzvSsICIiIlKcepRMm9kQYFs0ke4LfBb4hZnt4e6ropXpS4Cfd32s\nu5/d4XmmADVKpCVVHRPrdnXL1+7UK927xLTMt4iIiGRNTyvTQ4E7zKyESP/1fe7+ZzP7pZl9Ibpv\nlrs/DRDto57q7t9K58Xq6upWm9nyHsacjhHAihBeVzLArs76S+j6kHh0bUg8ujYkHl0buWNkKifl\n1aItYTGzJncfEnYckpt0fUg8ujYkHl0bEo+ujfzT49k8isS6sAOQnKbrQ+LRtSHx6NqQeHRt5Bkl\n06lpDjsAyWm6PiQeXRsSj64NiUfXRp5RMp2a2WEHIDlN14fEo2tD4tG1IfHo2sgz6pkWEREREUmT\nKtMiIiIiImlSMi0iIiIikiYl0yIiIiIiaVIyLSIiIiKSJiXTIiIiIiJpUjItIiIiIpImJdMiIiIi\nImlSMi0iIiIikiYl0yIiIiIiaVIyLSIiIiKSJiXTIiIiIiJpUjItIiIiIpKm0rAD6I6KigqvrKwM\nOwwRERERKXB1dXWr3X1IsvPyKpmurKyktrY27DBEREREpMCZ2fJUzsurZLpgXFcFzSsi3w8YAd9v\nCDceEREREUmLeqaD1jGRhsj311WFF4+IiIiIpE3JdNA6JtKJ9omIiIhIzlObR6544Hw44+awoxAR\nEZECt23bNhobG9m8eXPYoeSE8vJyhg8fTllZWVqPVzIdpHcWxj/26kNKpkVERCTrGhsb6d+/P5WV\nlZhZ2OGEyt1Zs2YNjY2NjBo1Kq3nUJtHkJ6/Pv6xtm3BxSEiIiJFa/PmzQwePLjoE2kAM2Pw4ME9\nqtIrmQ7S+0lm7Zh3eTBxiIiISFFTIr1DT38XSqaD5J74+Iu/DSYOERERkSJy++23s3Llyqw8t5Lp\nIPUdkPh429Zg4hAREREpIkqmC0VLCsny9CQJt4iIiEjQ3lkIf7828WQK3XDJJZfw29/uuCM/ffp0\nrr322pjn/vKXv+SII47g0EMP5fLLd7TEnnrqqYwbN45DDjmE2bNnA9Da2sqUKVMYM2YMVVVVXHfd\ndcyZM4fa2lrOPvtsqqur2bRpU0Z+hnaazSNIpb07b5eUQ2uMhvd4CXXFgfC9zFzEIiIiIjw+LfmY\nri0fwQeLwNvAesGeY6DPbvHP36sKPjcj4VNOnjyZiy++mAsvvBCA++67jyeeeGKn85566imWLFnC\nwoULcXe+9KUvMX/+fCZOnMjvf/97dt99dzZt2sQRRxzBGWecwbJly3j33XdZtGgRAOvWrWPgwIHc\ncMMNXHPNNdTU1CT+WdOgynSQulamB43s3uNXvxFJtB84P3MxiYiIiCSyuTmSSEPkv5ube/yUY8eO\nZdWqVaxcuZJXXnmFQYMGMWLEiJ3Oe+qpp3jqqacYO3Yshx9+OK+//jpLliwB4Ne//jWHHXYYRx55\nJO+88w5Llixh3333ZenSpVx00UU88cQT7LZbgqQ/Q5JWps1sH+BOYC+gDZjt7teb2SRgOnAQMN7d\na+M8fiBwCzAGcOA/3P1FM5sOnA80RU+9zN0f69mPk+N22b3z9q4VsNvesPTp7j1Pw33QMAemr81c\nbCIiIlJ8klSQgUhrxx1fgtatUNIbzrgF9hnf45c+88wzmTNnDu+//z6TJ0+OeY67c+mll/Ltb3+7\n0/5nn32Wv/zlL7z44ovssssuHHvssWzevJlBgwbxyiuv8OSTT3LjjTdy33338fvf/77HsSaSSptH\nC/BDd/+nmfUH6sxsHrAIOB34XZLHXw884e5nmllvYJcOx65z92vSCTwvtbZ03u47CCb/EWYfByvr\nuvlkbZEqddVXtNiLiIiIZM8+4+G8R2DZ36HymIwk0hBp9Tj//PNZvXo1f/vb32Kec9JJJ/HTn/6U\ns88+m379+vHuu+9SVlZGc3MzgwYNYpddduH111/nH//4BwCrV6+md+/enHHGGey3335MmTIFgP79\n+7N+/fqMxN1V0mTa3d8D3ot+v97MFgN7u/s8SDw3n5ntBkwEpkQfvxUozikr3lkI774U+9gFT0eO\n33oSkeJ/NzTcB6/9CX66qschioiIiMS0z/iMJdHtDjnkENavX8/ee+/N0KFDY55z4oknsnjxYj75\nyU8C0K9fP+666y5OPvlkbrrpJg499FAOPPBAjjzySADeffddvvGNb9DWFsmn/ud//geAKVOmMHXq\nVPr27cuLL75I3759M/ZzmCeb+7jjyWaVwHxgjLt/FN33LPCjWG0eZlYNzAZeAw4D6oD/dPeN0TaP\nKcBHQC2R6vdOfQtmdgFwAcCIESPGLV++POV4c8qfvw+1XW4z1HwDvjAz+WOvq4LmFcnPm97zHiYR\nEREpbIsXL+aggw4KO4ycEut3YmZ17p50xGLKAxDNrB/wAHBxeyKdglLgcGCWu48FNgLTosdmAfsB\n1UQq3zHnQ3H32e5e4+41Q4YMSTXc3LOha+XY4LCzUnvs9xsiiXJJn8TnTR+QsSlrRERERCS5lJJp\nMysjkkj/0d0f7MbzNwKN7r4guj2HSHKNu3/g7q3u3gbcDGT23kGuG3lU92+X/HQVfOH6xOfceoKW\nJRcREZG80tDQQHV1daevCRMmhB1WSlKZzcOAW4HF7v6r7jy5u79vZu+Y2YHu/gZwPJGWD8xsaLQf\nG+A0IgMaC9emDM28UTMl8jV9IJHJUWJ4fia89y8496HMvKaIiIhIFlVVVVFfXx92GGlJpTL9KeAc\n4Dgzq49+fd7MTjOzRuCTwFwzexLAzIaZWccp7i4C/mhm/yLS0nF1dP//mllDdP9ngO9n6ofKSRtX\nJ97urunrYNc94x9f+nRklhARERERyZpUZvN4Dog3ZcdOpU93Xwl8vsN2PbBT87a7n5N6mAVg14rI\noisdt3vqx29GWjqejzOIcWVdJKG+oJvzWIuIiEhBc/eEM7IVk+5MxhGLVkAMSt9BibfTdcIViWfx\nWFkHd56WmdcSERGRvFdeXs6aNWt6nEQWAndnzZo1lJeXp/0cqSzaIvlgenNkNo9Ylj4dqWCfcEWw\nMYmIiEjOGT58OI2NjTQ1NSU/uQiUl5czfPjwtB+vZDoomz7ssp2FpcATJdTPz4TRp2R8wnURERHJ\nL2VlZYwaNSrsMAqG2jyCsqHLp7+eDkCMJ1HLx60nZOc1RURERIqUkumg9OnXeTsTAxDjSZRQx6tc\ni4iIiEi3KZkOyqYuCW6mBiDGo4RaREREJOuUTAeh9nZYu7Tzvn4BLI3+zXnxj12xe/ZfX0RERKTA\nKZkOwst37rzvsLOy/7r7jIeqr8Q+5q3wywOyH4OIiIhIAVMyHYTSLnMX7lUV3KwaZ9wMFQfGPrbx\ng8iUeSIiIiKSFiXTQejaHz1wZLCv/72FUB6nRzve6okiIiIikpSS6SB0nVM6G3NMJzNtGVhJ7GMa\nkCgiIiKSFiXTQeg6p3S25phO5vIP4x+bPjC4OEREREQKhJLpIHSdUzqbc0wnE3fKPIcZlUFGIiIi\nIpL3lEwXoy9cH3v/5rUakCgiIiLSDUqmg7AxoKXEU1UzJf4MHxqQKCIiIpIyJdOBsM6bpb3DCaOj\n7y2Ekj6xj2lAooiIiEhKSpOdYGb7AHcCewFtwGx3v97MJgHTgYOA8e5eG+fxA4FbgDGAA//h7i+a\n2e7AvUAlsAz4iruHMM1FADau6rzdsjWcOLr66ar4ifN/7xE5LoXvgfOh4b6eP0/5oMisMSIiIkUk\naTINtAA/dPd/mll/oM7M5gGLgNOB3yV5/PXAE+5+ppn1BnaJ7p8G/NXdZ5jZtOj2JWn9FLms9vad\np8Kr2D+UUGKa3hw7oW7dArPaC+OQAAAgAElEQVSPgwueDj4mya5fHhBZsCfTNq/d+VoaNk7XkIiI\nFLSkybS7vwe8F/1+vZktBvZ293kAZhb3sWa2GzARmBJ9/FagvSz7ZeDY6Pd3AM9SiMl0rKXEP3Vx\n8HEkUvWV2JXJlXXwzsLgVmuU7Ll6OGxdH/zrrqzbkWBbSeLpGUVERPJQKpXp7cysEhgLLEjxIfsC\nTcBtZnYYUAf8p7tvBPaMJuq4+3tmtkd3YskbrV1aOnbfN/eS0zNuhiXzIpXFrm49IcF0epLT7jwN\nluZQVdhbO1SuDb75VO79WxAREemmlAcgmlk/4AHgYnf/KMWHlQKHA7PcfSywkUg7R8rM7AIzqzWz\n2qampuQPyDWbu/yq2lrDiSOZacuIezlcGeK82NJ9MyojSWsuJdI78egHtQGRqrmIiEieSqkybWZl\nRBLpP7r7g914/kag0d3bK9lz2JFMf2BmQ6NV6aFAzNFu7j4bmA1QU1Pj3Xjt3OCeeDuXTI/R8wrQ\ntk390/mgp60cvfvDZY3df1xPK+Bb1++47vY9Ds59KP3nEhERCVgqs3kYcCuw2N1/1Z0nd/f3zewd\nMzvQ3d8Ajgdeix5+BDgPmBH975+6FXm+6DsAmrts57IvXA9//s+d96t/OnfNqIzdopNMpgYHxkp+\n0x3kuPTpSGKtmUFERCRPmCeplJrZ0cDfgQYiU+MBXAb0AX4DDAHWAfXufpKZDQNucffPRx9fTWRq\nvN7AUuAb7r7WzAYD9wEjgBXAJHdPODqppqbGa2tjzsCXu2ZWwboVO7YHjoSL/xVePKm4rgqaV8Q+\npv7p3DH7uMiHnO6o+kqkRz5oV+we6ZnuNvVWi4hIOMyszt1rkp6XLJnOJXmZTF+9N2zdsGO7317w\nozfCiydV0wex47NTR70i7SASnncWRvqNU5VrVd4rKyKtQ90V1gcBEREpSqkm01oBMZtqb++cSAOU\n53ibR7u4CXNb5Ba+hOOqoakn0vseF7mTkEuJNMDPVkfiqvpK9x7XcF+kBeQGValFRCR3qDKdTTdO\ngKbXO+/7wvVQMyWUcLotUQX0UxfDCVcEG08x684qhflYwU2n73vXPeHHb2YlHAnJDeNhddB37tRK\nJCKxqc0jF1xzIGx4f8d2urMlhClRX676p4ORar9xIcyEkc7MIKW7wE/ey048knnpDpgN04AR8P2G\nsKMQkYApmc4Fv6jsvJR430FwybKwoklfoh5XJdTZk2o1ulArtN3tre5VFmkhkdxQe3vsmYEKTSF8\niBWRmJRM54L/HtJ5BcTScvhJGtOF5YJY808DlPSBn8acIlx6IqVE0mD6ukDCCVU6lUy1IQUvHyvO\n2VSoH3Il8YxXmaQ7IqFTMh22WP3GJb3hp3m4iiMk7p+uOBC+tzDYeApZvA8uHeVjX3RPpfMHTFXD\n7PnvPaB1S9hR5J98bPcrJOnOJlQo1BbXLUqmMyWTtyr7DIBLA/g0my2J2g7yaWBlrkpl8JVaGdKb\nXzvXpgfMRz1dYbM7gqrI5VRipYGQaenO4GzJnCL5UKhkOhMy3fNXCLeeE93KVf90+lKpRhfC9ZNJ\n8y6H52d27zH6MJK6bM+skQ93V0KZXSSOYitYpLuKqhSmkAoiSqYz4Q+nwdsZWG65XaEkm9MHAnGu\nm0L5GYOS0gIsWignoXcWwq0nEXuRoQQytZx6ocjWgMFCHVeRa8lePvye1RokPRFCQq1kOhMy+cel\n0AYSxKukqvKXulTaFdTz2z1XDYWWj7v3mGK+ZtP5fSWTDxXnbEqnDUnyU7bGC+XSHZFcE3DBTsl0\npmQioS60RBoSV1TVn5pcKnNHq8qfvnRnlij0PsCM/5FWn2/K1NubQ4rwuk2nLS7XqDKdGXk1m0cx\nSLTAhiqq8SXrj9Zo68xJZxGYdoXwobAnP388xV55zga1P/RcoX8QzhVhfShUz3TmKJnOQYkqgN+c\nV1yf/JNJ5U1IiUp2vLMQbj2RuL3+yVgJXP5hRkPKimzcHi7EO2v5pNgTbRVmJERKpiU4iVoW1KoQ\nkcofRP2ugpGJgWO50GetAYMC+bnSZLHNTCJ5S8m0BCtR60KxJ4nJ2jpyITErRunOAhJXlvowMx5n\nDJp2UURkJ0qmJXhKqDtLpWKkW5i5odgGh2nVUhGRpJRMS/CSzZlcTAl1KktfF9PvI58UYmK9657w\n4zfDjkJEJK9kLJk2s32AO4G9iNxnnO3u15vZJGA6cBAw3t1jZrlmtgxYD7QCLe1Bmdl04HygKXrq\nZe7+WKJYlEzngWTT7xRDAploURtAi7DkmZxacjpFGjQoItJjqSbTpSk8VwvwQ3f/p5n1B+rMbB6w\nCDgd+F0Kz/EZd4/VFHqdu1+TwuMlX5xwBbz3r/jTcU0fCNPXBRtTUFJZzVBJTv7p2M/e01lBskED\nBkVEQpU0mXb394D3ot+vN7PFwN7uPg/AzLIboeSfcx9K0ObghZlQpzIlmUaw5799xse+doOoXmug\nqohITkqlMr2dmVUCY4EF3XiYA0+ZmQO/c/fZHY59z8zOBWqJVL9177tQfL8Brh4OW9fHOOiRwYqF\n0vKRtK2DwvlZJTYluSIiRatXqieaWT/gAeBid/+oG6/xKXc/HPgc8F0zmxjdPwvYD6gmUvm+Ns7r\nXmBmtWZW29TUFOsUyVWXNUZW84sn2ZRxuW7e5dGfIUEiXbqLEmkREZECllIybWZlRBLpP7r7g915\nAXdfGf3vKuAhYHx0+wN3b3X3NuDm9v0xHj/b3WvcvWbIkCHdeWnJBT95rzAT6quGJh5oCZHVDLUs\nuIiISEFLmkxbpCn6VmCxu/+qO09uZrtGBy1iZrsCJxIZuIiZDe1w6mnt+6UApZJQ194eWDg9Unt7\nJN6WjxOfN71Zy4KLiIgUgVSmxjsa+DvQwI4luC4D+gC/AYYA64B6dz/JzIYBt7j7581sXyLVaIj0\nZ9/t7j+PPu8fiLR4OLAM+HZ0sGNcmhovz8XtoY7K9ZkurhqaPIku3UXVaBERkQKgRVskN/3yANj4\nQYITLPdm+kh1EQ8tySwiIlIwUk2mUx6AKJIRP34Tho1LcEJ0po95lwcWUkLTB6SWSE9vViItIiJS\nhJRMS/AueDoy53Iiz8+EK3YPJp5Yrhqa2uDIYeM0W4eIiEgRU5uHhCuVhLXiQPjewuzHAsn7ujtS\nEi0iIlKw1OYh+WF6c2Q55ERWvxFJuq+ryk4M7yyMrso4ILVEet/jlEiLiIgI0M0VEEWy4qerUhvk\n17wikvBmalnlGZWwuRuLbvbuH1mIRkRERCRKbR6SW67YHby1e4+p+kpqczrPuzz5QivxqBItIiJS\nVFJt81BlWnLL5R92P+ltuC+1GTfSoenuREREJAH1TEvuOeGKSCV4wIjwYvjUxZruTkRERJJSZVpy\nV/tqiDeMjwxCzLZM9WKLiIhI0VAyLbmvfVq8dxbCrScSWYE+g1LtuRYRERHpQsm05I99xndearw7\nc0J3VLoL/OS9zMUlIiIiRUvJtOQvTVMnIiIiIcurqfHMrAlYHsJLjwBWhPC6kh90fUg8ujYkHl0b\nEo+ujdwx0t2HJDspr5LpsJhZUyq/TClOuj4kHl0bEo+uDYlH10b+0dR4qVmX/BQpYro+JB5dGxKP\nrg2JR9dGnlEynRotfyeJ6PqQeHRtSDy6NiQeXRt5Rsl0amaHHYDkNF0fEo+uDYlH14bEo2sjz6hn\nWkREREQkTapMi4iIiIikScm0iIiIiEialEyLiIiIiKRJybSIiIiISJqUTIuIiIiIpEnJtIiIiIhI\nmpRMi4iIiIikScm0iIiIiEialEyLiIiIiKRJybSIiIiISJqUTIuIiIiIpKk07AC6o6KiwisrK8MO\nQ0REREQKXF1d3Wp3H5LsvLxKpisrK6mtrQ07DBEREREpcGa2PJXz1OYRoGnzp3H0/x3NtPnTwg5F\nRERERDJAyXRAps2fxtx/z6V5azNz/z2Xs/58VtghiYiIiEgPKZkOyJPLnuy03bCmgfvfuD+kaERE\nREQkE/KqZzqftXnbTvvuWnwXkw6cFEI0IiIiUgy2bdtGY2MjmzdvDjuUnFVeXs7w4cMpKytL6/FK\npgPSv3d/mrc2d9r30ZaPQopGREREikFjYyP9+/ensrISMws7nJzj7qxZs4bGxkZGjRqV1nNkpc3D\nzH5vZqvMbFGc48eaWbOZ1Ue/fpaNOHLJnrvsudO+3iW9Q4hEREREisXmzZsZPHiwEuk4zIzBgwf3\nqHKfrcr07cANwJ0Jzvm7u38hS6+fc7a0btlp39Bdh4YQiYiIiBQTJdKJ9fT3k5XKtLvPBz7MxnPn\nK2Pn/1ED+gwIIRIRERERyZQwZ/P4pJm9YmaPm9kh8U4yswvMrNbMapuamoKML2PqV9WzfH1K836L\niIiISB4JK5n+JzDS3Q8DfgM8HO9Ed5/t7jXuXjNkSNIVHXPSI28/guNhhyEiIiKSF6ZMmcKcOXPC\nDiMloSTT7v6Ru2+Ifv8YUGZmFWHEEoRYLR4iIiIiuah+VT23NNxC/ar6sEPJC6FMjWdmewEfuLub\n2XgiSf2aMGIJwujdR4cdgoiIiBS5Xyz8Ba9/+HrCczZs3cAba9/AcQzjwEEH0q93v7jnj959NJeM\nvyTu8UsuuYSRI0dy4YUXAjB9+nT69+/PD3/4w07nuTsXXXQRTz/9NKNGjcJ9xx39v/71r/zoRz+i\npaWFI444glmzZvHKK68wY8YMHnzwQf70pz8xefJkmpubaWtr4+CDD2bp0qUce+yxTJgwgWeeeYZ1\n69Zx6623cswxx6Tyq+qWbE2N93/Ai8CBZtZoZt80s6lmNjV6ypnAIjN7Bfg1MNk7/tYKzOIPF4cd\ngoiIiEhS67et396a6jjrt63v0fNNnjyZe++9d/v2fffdx6RJOy9Y99BDD/HGG2/Q0NDAzTffzAsv\nvABEpvabMmUK9957Lw0NDbS0tDBr1iwOP/xwXn75ZQD+/ve/M2bMGF566SUWLFjAhAkTtj9vS0sL\nCxcuZObMmVxxxRU9+lniyUpl2t2/luT4DUSmzisKazYVbNFdRERE8kSiCnK7+lX1nP/U+Wxr20ZZ\nrzJmHDOD6j2q037NsWPHsmrVKlauXElTUxODBg1ixIgRO503f/58vva1r1FSUsKwYcM47rjjAHjj\njTcYNWoUBxxwAADnnXceN954IxdffDH7778/ixcvZuHChfzgBz9g/vz5tLa2dqo+n3766QCMGzeO\nZcuWpf1zJKIVEANQ0bdg28FFRESkgFTvUc3NJ95M7Qe11OxZ06NEut2ZZ57JnDlzeP/995k8eXLc\n82LN95yoceGYY47h8ccfp6ysjM9+9rNMmTKF1tZWrrnmmu3n9OnTB4CSkhJaWlp68FPEF+bUeEUj\nXs/0/Mb5au4XERGRnFK9RzXfqvpWRhJpiLR63HPPPcyZM4czzzwz5jkTJ07knnvuobW1lffee49n\nnnkGgNGjR7Ns2TLeeustAP7whz/w6U9/evtjZs6cySc/+UmGDBnCmjVreP311znkkLgzLmeFKtMB\niNcz3eItPPr2oxm7WEVERERyzSGHHML69evZe++9GTo09urPp512Gk8//TRVVVUccMAB2xPm8vJy\nbrvtNiZNmrR9AOLUqZEheBMmTOCDDz5g4sSJABx66KHssccega/4qGQ6AImmxtP80yIiIlLoGhoa\nEh43M264IfZwuuOPP377YMOO+vbty5YtW7Zvz549u9PxZ599dvv3FRUVWeuZVptHABJNjXfQ7gcF\nGImIiIiIZJIq0wFINDVesvkeRURERApFQ0MD55xzTqd9ffr0YcGCBSFF1HNKpgOgNg8REREJi7sH\n3kccT1VVFfX1uTX5Qk+XOlGbRwDU5iEiIiJhKC8vZ82aNT1OGAuVu7NmzRrKy8vTfg5VpgPQvLU5\n5n7D4h4TERER6anhw4fT2NhIU1NT2KHkrPLycoYPH57245VMB2BA7wEx9zse95iIiIhIT5WVlTFq\n1KiwwyhoavMIgAYgioiIiBQmJdMBaPO2uMc0AFFEREQkfymZDsB+A/aLe0wDEEVERETyV1aSaTP7\nvZmtMrNFcY6bmf3azN4ys3+Z2eHZiCNXrN68OuZ+DUAUERERyW/ZqkzfDpyc4PjngE9Evy4AZmUp\njpzQt7RvzP0agCgiIiKS37KSTLv7fODDBKd8GbjTI/4BDDSzodmIJRd8uDn+r0IDEEVERETyV1g9\n03sD73TYbozu24mZXWBmtWZWm69zJJb3ij8RuAYgioiIiOSvsJLpWGtaxswq3X22u9e4e82QIUOy\nHFZ2vN38dtxjGoAoIiIikr/CSqYbgX06bA8HVoYUS1bVr6rn+ZXPb98usZLt32sAooiIiEh+CyuZ\nfgQ4Nzqrx5FAs7u/F1IsWVX7QW2neaarh1Rv/14DEEVERETyW1aWEzez/wOOBSrMrBG4HCgDcPeb\ngMeAzwNvAR8D38hGHLlgQO8BnfqiB/TZkTyrMi0iIiKS37KSTLv715Icd+C72XjtXNMxWbYureKq\nTIuIiIjkN62AmGUdk2XHad7SuRKtqfFERERE8peS6SzrWpne2ra103FNjSciIiKSv5RMZ1nXyvSI\n/iM6HdfUeCIiIiL5S8l0li3+cHGn7eXrl3fqnVabh4iIiEj+UjKdZV0HHe7Rdw9Ke+0Y9/ngkgep\nX1UfdFgiIiIikgFKprNs9O6jO20fvffRTNhrwvbtFm/h0bcfDTosEREREckAJdNZ1rXNY/GHi9lj\nlz067dMgRBEREZH8pGQ6y7q2eRjGIRWHdNqnQYgiIiIi+UnJdJZ1bfMYvftoPtr60fZtrYIoIiIi\nkr+UTGdZrDaPrtPlaRVEERERkfykZDrLYrV5dJ0OT9PjiYiIiOQnJdNZFqvNo+uAQw1AFBEREclP\nSqazLFabR9cBhxqAKCIiIpKfspZMm9nJZvaGmb1lZtNiHJ9iZk1mVh/9+la2YglTm7d12labh4iI\niEjhyEoybWYlwI3A54CDga+Z2cExTr3X3aujX7dkI5aw7Ttg307bavMQERERKRzZqkyPB95y96Xu\nvhW4B/hyll4rp7265tVO22rzEBERESkc2Uqm9wbe6bDdGN3X1Rlm9i8zm2Nm+8R6IjO7wMxqzay2\nqakpG7Fm1epNqzttr9m0Rm0eIiIiIgUiW8m0xdjXtZfhUaDS3Q8F/gLcEeuJ3H22u9e4e82QIUMy\nHGb2tba1dtqu6FuxU4LddVtERERE8kO2kulGoGOleTiwsuMJ7r7G3bdEN28GxmUpltDUr6qnflX9\n9u1SK+WL+32RwX0Hdzqv67aIiIiI5IdsJdMvAZ8ws1Fm1huYDDzS8QQzG9ph80tA5znkCsAjbz9C\nKzsq0xOHT6R6j2r1TIuIiIgUiNJsPKm7t5jZ94AngRLg9+7+qpldCdS6+yPA/zOzLwEtwIfAlGzE\nEqY1m9bE3K+eaREREZHCkJVkGsDdHwMe67LvZx2+vxS4NFuvn8vUMy0iIiJSGLQCYhZV9K2Iua2e\naREREZHCoGQ6i0bvPjrmdtce6X5l/QKLSUREREQyR8l0Fi3+cHHM7eatzZ323/nqnZ1m/RARERGR\n/KBkOou6DkBs367Zs4ZeHX71rbTy6NuPBhqbiIiIiPSckukQVO9RzcGDD+60T4MQRURERPKPkumQ\n7F6+e9ghiIiIiEgPKZkOSWmvrM1KKCIiIiIBUTItIiIiIpImJdNZtHbz2k7bzVua45wpIiIiIvlI\nyXQWfbj5w07ba7esjXOmiIiIiOQjNe5m0ZbWLZ22B/UZFFIkEoYj/nAEm9s2B/qap4w6hRkTZwT6\nmiIiIsVMyXSW3P/G/bz/8fud9u03cL/t33dt+VALSP64/437ufIfV4YdRkxz/z2Xuf+em9K5SrxF\nRER6Tsl0lty1+K6d9n1xvy9u/75ry0fH7XF3jmOrb92+3dt6U3duXRailETCqCwHKVniXUopL5/3\ncoARiYiI5J+sJdNmdjJwPVAC3OLuM7oc7wPcCYwD1gBfdfdl2YonaB9t+ajT9oDeA6jeo3r7dteW\nj/btqjuqdnqurb6VqjuqqOhTwTOTn8lCtMXtyw99maUfLQ07jJzTQkvM67GjbxzyDX5Q84OAIpKO\nzvrzWTSsaQg7jFD97MifMenASWGHISJFztw9809qVgK8CZwANAIvAV9z99c6nHMhcKi7TzWzycBp\n7v7VRM9bU1PjtbW1GY83kUzd0q8or+CZr+5IhKc8PoW6VTuqzSP6j2DNx2vY2Lox6XMNKBvAc2c9\n1+OYitFn7vkMq7dotcmg7FqyK//4+j/CDiNnKSHOfUcNPYrfnfi7sMPImJPuP4mVH68MOwyRbgkr\n7zGzOnevSXZetirT44G33H1pNJh7gC8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb754bc6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['v_north', 'v_east', 'v_down'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7570494a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['p', 'q', 'r'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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b8M4e9jsxIt4N/AH4fErphR72kSRJpVaOGfJ648gVakDFBOboYV3qtvwT4IaU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\nOBAg2zpwEXBhdnlzVYpVRXX6B2wEsA4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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7545ec668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['alpha', 'beta', 'TAS'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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VKMaqAC5902ze8uL6fkvXKrouvpUnNm4ruowxwZv2Rmaoe6m094qYgx0RizOze0THNlLA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\n6PKv08vt84EfZubRwA/L2y3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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7540774e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['Fx', 'Fy', 'Fz'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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ueSeOCzAqERERERkM7eQYoHknjuPE4pFdxznhkEpERERERDKcEuwAVe6oZ0fdu2XpHfHn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\nyaIEO0DrqrvXXD+89eGAIhERERGRZFG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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb74d48b9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['Mx', 'My', 'Mz'], **kwargs);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/asaez/miniconda3/envs/pyfme/lib/python3.6/site-packages/pandas/plotting/_core.py:1714: UserWarning: Pandas doesn't allow columns to be created via a new attribute name - see https://pandas.pydata.org/pandas-docs/stable/indexing.html#attribute-access\n",
      "  series.name = label\n"
     ]
    },
    {
     "data": {
      "image/png": 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sX76cX//61+usra8GYp3qB4BtI2IS8AxwHHBCZmZE3AEcTWme9cnAjQNQjyRJ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\nxyPinG72nxIRbRExv/z1mU7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fb7570c6908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results.plot(y=['elevator', 'aileron', 'rudder', 'thrust'], **kwargs);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Propagating only one time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "dt = 0.05  # seconds\n",
    "sim = Simulation(aircraft, system, environment, controls, dt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "time: 100%|█████████▉| 0.49999999999999994/0.5 [00:00<00:00,  4.02it/s]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Fx</th>\n",
       "      <th>Fy</th>\n",
       "      <th>Fz</th>\n",
       "      <th>Mach</th>\n",
       "      <th>Mx</th>\n",
       "      <th>My</th>\n",
       "      <th>Mz</th>\n",
       "      <th>TAS</th>\n",
       "      <th>a</th>\n",
       "      <th>aileron</th>\n",
       "      <th>...</th>\n",
       "      <th>thrust</th>\n",
       "      <th>u</th>\n",
       "      <th>v</th>\n",
       "      <th>v_down</th>\n",
       "      <th>v_east</th>\n",
       "      <th>v_north</th>\n",
       "      <th>w</th>\n",
       "      <th>x_earth</th>\n",
       "      <th>y_earth</th>\n",
       "      <th>z_earth</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>time</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.05</th>\n",
       "      <td>1.716671e-11</td>\n",
       "      <td>2.641222e-16</td>\n",
       "      <td>2.182787e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.459194e-14</td>\n",
       "      <td>-1.360312e-11</td>\n",
       "      <td>8.035347e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.371463e-16</td>\n",
       "      <td>1.332268e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.10</th>\n",
       "      <td>1.739409e-11</td>\n",
       "      <td>1.000965e-15</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.976768e-14</td>\n",
       "      <td>-1.164692e-11</td>\n",
       "      <td>7.251039e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.369266e-16</td>\n",
       "      <td>2.664535e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.15</th>\n",
       "      <td>1.739409e-11</td>\n",
       "      <td>2.337016e-15</td>\n",
       "      <td>2.728484e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.678983e-14</td>\n",
       "      <td>-9.240578e-12</td>\n",
       "      <td>6.009923e-16</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.365954e-16</td>\n",
       "      <td>3.552714e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.20</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>3.932746e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.365093e-14</td>\n",
       "      <td>-6.789590e-12</td>\n",
       "      <td>1.213662e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.357530e-16</td>\n",
       "      <td>4.884981e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.25</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>5.945782e-15</td>\n",
       "      <td>3.637979e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.163916e-14</td>\n",
       "      <td>-5.474300e-12</td>\n",
       "      <td>1.650906e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.346854e-16</td>\n",
       "      <td>6.661338e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.30</th>\n",
       "      <td>1.807621e-11</td>\n",
       "      <td>8.315261e-15</td>\n",
       "      <td>4.001777e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.020804e-14</td>\n",
       "      <td>-3.640737e-12</td>\n",
       "      <td>2.051842e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.330276e-16</td>\n",
       "      <td>7.993606e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.35</th>\n",
       "      <td>1.841727e-11</td>\n",
       "      <td>1.098849e-14</td>\n",
       "      <td>4.365575e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>9.148544e-15</td>\n",
       "      <td>-2.045869e-12</td>\n",
       "      <td>1.306538e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.307814e-16</td>\n",
       "      <td>9.769963e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>13</td>\n",
       "      <td>7</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.40</th>\n",
       "      <td>1.875833e-11</td>\n",
       "      <td>1.383942e-14</td>\n",
       "      <td>4.729372e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>7.977795e-15</td>\n",
       "      <td>-1.049373e-12</td>\n",
       "      <td>7.766174e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.281022e-16</td>\n",
       "      <td>1.199041e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.45</th>\n",
       "      <td>1.887202e-11</td>\n",
       "      <td>1.687040e-14</td>\n",
       "      <td>5.275069e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>7.010262e-15</td>\n",
       "      <td>1.565743e-13</td>\n",
       "      <td>1.094014e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.252482e-16</td>\n",
       "      <td>1.421085e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>17</td>\n",
       "      <td>9</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.50</th>\n",
       "      <td>1.944045e-11</td>\n",
       "      <td>2.009447e-14</td>\n",
       "      <td>5.456968e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>6.310511e-15</td>\n",
       "      <td>8.749163e-13</td>\n",
       "      <td>1.579341e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.221523e-16</td>\n",
       "      <td>1.643130e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>19</td>\n",
       "      <td>10</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Fx            Fy            Fz      Mach            Mx  \\\n",
       "time                                                                     \n",
       "0.05  1.716671e-11  2.641222e-16  2.182787e-11  0.133756  2.459194e-14   \n",
       "0.10  1.739409e-11  1.000965e-15  2.364686e-11  0.133756  1.976768e-14   \n",
       "0.15  1.739409e-11  2.337016e-15  2.728484e-11  0.133756  1.678983e-14   \n",
       "0.20  1.762146e-11  3.932746e-15  2.910383e-11  0.133756  1.365093e-14   \n",
       "0.25  1.762146e-11  5.945782e-15  3.637979e-11  0.133756  1.163916e-14   \n",
       "0.30  1.807621e-11  8.315261e-15  4.001777e-11  0.133756  1.020804e-14   \n",
       "0.35  1.841727e-11  1.098849e-14  4.365575e-11  0.133756  9.148544e-15   \n",
       "0.40  1.875833e-11  1.383942e-14  4.729372e-11  0.133756  7.977795e-15   \n",
       "0.45  1.887202e-11  1.687040e-14  5.275069e-11  0.133756  7.010262e-15   \n",
       "0.50  1.944045e-11  2.009447e-14  5.456968e-11  0.133756  6.310511e-15   \n",
       "\n",
       "                My            Mz   TAS           a       aileron   ...     \\\n",
       "time                                                               ...      \n",
       "0.05 -1.360312e-11  8.035347e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.10 -1.164692e-11  7.251039e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.15 -9.240578e-12  6.009923e-16  45.0  336.434581  2.492525e-18   ...      \n",
       "0.20 -6.789590e-12  1.213662e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.25 -5.474300e-12  1.650906e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.30 -3.640737e-12  2.051842e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.35 -2.045869e-12  1.306538e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.40 -1.049373e-12  7.766174e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.45  1.565743e-13  1.094014e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.50  8.749163e-13  1.579341e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "\n",
       "        thrust         u             v        v_down     v_east    v_north  \\\n",
       "time                                                                         \n",
       "0.05  0.577997  44.87164  8.371463e-16  1.332268e-15  21.574149  39.491215   \n",
       "0.10  0.577997  44.87164  8.369266e-16  2.664535e-15  21.574149  39.491215   \n",
       "0.15  0.577997  44.87164  8.365954e-16  3.552714e-15  21.574149  39.491215   \n",
       "0.20  0.577997  44.87164  8.357530e-16  4.884981e-15  21.574149  39.491215   \n",
       "0.25  0.577997  44.87164  8.346854e-16  6.661338e-15  21.574149  39.491215   \n",
       "0.30  0.577997  44.87164  8.330276e-16  7.993606e-15  21.574149  39.491215   \n",
       "0.35  0.577997  44.87164  8.307814e-16  9.769963e-15  21.574149  39.491215   \n",
       "0.40  0.577997  44.87164  8.281022e-16  1.199041e-14  21.574149  39.491215   \n",
       "0.45  0.577997  44.87164  8.252482e-16  1.421085e-14  21.574149  39.491215   \n",
       "0.50  0.577997  44.87164  8.221523e-16  1.643130e-14  21.574149  39.491215   \n",
       "\n",
       "             w  x_earth  y_earth  z_earth  \n",
       "time                                       \n",
       "0.05  3.396464        1        1    -1000  \n",
       "0.10  3.396464        3        2    -1000  \n",
       "0.15  3.396464        5        3    -1000  \n",
       "0.20  3.396464        7        4    -1000  \n",
       "0.25  3.396464        9        5    -1000  \n",
       "0.30  3.396464       11        6    -1000  \n",
       "0.35  3.396464       13        7    -1000  \n",
       "0.40  3.396464       15        8    -1000  \n",
       "0.45  3.396464       17        9    -1000  \n",
       "0.50  3.396464       19       10    -1000  \n",
       "\n",
       "[10 rows x 35 columns]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = sim.propagate(0.5)\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can propagate for one time step even once the simulation has been propagated before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "time: 100%|██████████| 0.55/0.55 [00:00<00:00, 73.33it/s]\n"
     ]
    },
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Fx</th>\n",
       "      <th>Fy</th>\n",
       "      <th>Fz</th>\n",
       "      <th>Mach</th>\n",
       "      <th>Mx</th>\n",
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       "      <th>Mz</th>\n",
       "      <th>TAS</th>\n",
       "      <th>a</th>\n",
       "      <th>aileron</th>\n",
       "      <th>...</th>\n",
       "      <th>thrust</th>\n",
       "      <th>u</th>\n",
       "      <th>v</th>\n",
       "      <th>v_down</th>\n",
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       "      <th>z_earth</th>\n",
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       "    <tr>\n",
       "      <th>time</th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.05</th>\n",
       "      <td>1.716671e-11</td>\n",
       "      <td>2.641222e-16</td>\n",
       "      <td>2.182787e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>2.459194e-14</td>\n",
       "      <td>-1.360312e-11</td>\n",
       "      <td>8.035347e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.371463e-16</td>\n",
       "      <td>1.332268e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>-1000</td>\n",
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       "    <tr>\n",
       "      <th>0.10</th>\n",
       "      <td>1.739409e-11</td>\n",
       "      <td>1.000965e-15</td>\n",
       "      <td>2.364686e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.976768e-14</td>\n",
       "      <td>-1.164692e-11</td>\n",
       "      <td>7.251039e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.369266e-16</td>\n",
       "      <td>2.664535e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.15</th>\n",
       "      <td>1.739409e-11</td>\n",
       "      <td>2.337016e-15</td>\n",
       "      <td>2.728484e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.678983e-14</td>\n",
       "      <td>-9.240578e-12</td>\n",
       "      <td>6.009923e-16</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.365954e-16</td>\n",
       "      <td>3.552714e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.20</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>3.932746e-15</td>\n",
       "      <td>2.910383e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.365093e-14</td>\n",
       "      <td>-6.789590e-12</td>\n",
       "      <td>1.213662e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.357530e-16</td>\n",
       "      <td>4.884981e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
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       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>-1000</td>\n",
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       "    <tr>\n",
       "      <th>0.25</th>\n",
       "      <td>1.762146e-11</td>\n",
       "      <td>5.945782e-15</td>\n",
       "      <td>3.637979e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.163916e-14</td>\n",
       "      <td>-5.474300e-12</td>\n",
       "      <td>1.650906e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.346854e-16</td>\n",
       "      <td>6.661338e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>9</td>\n",
       "      <td>5</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.30</th>\n",
       "      <td>1.807621e-11</td>\n",
       "      <td>8.315261e-15</td>\n",
       "      <td>4.001777e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>1.020804e-14</td>\n",
       "      <td>-3.640737e-12</td>\n",
       "      <td>2.051842e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.330276e-16</td>\n",
       "      <td>7.993606e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>11</td>\n",
       "      <td>6</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.35</th>\n",
       "      <td>1.841727e-11</td>\n",
       "      <td>1.098849e-14</td>\n",
       "      <td>4.365575e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>9.148544e-15</td>\n",
       "      <td>-2.045869e-12</td>\n",
       "      <td>1.306538e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.307814e-16</td>\n",
       "      <td>9.769963e-15</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>13</td>\n",
       "      <td>7</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.40</th>\n",
       "      <td>1.875833e-11</td>\n",
       "      <td>1.383942e-14</td>\n",
       "      <td>4.729372e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>7.977795e-15</td>\n",
       "      <td>-1.049373e-12</td>\n",
       "      <td>7.766174e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.281022e-16</td>\n",
       "      <td>1.199041e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>15</td>\n",
       "      <td>8</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.45</th>\n",
       "      <td>1.887202e-11</td>\n",
       "      <td>1.687040e-14</td>\n",
       "      <td>5.275069e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>7.010262e-15</td>\n",
       "      <td>1.565743e-13</td>\n",
       "      <td>1.094014e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.252482e-16</td>\n",
       "      <td>1.421085e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>17</td>\n",
       "      <td>9</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.50</th>\n",
       "      <td>1.944045e-11</td>\n",
       "      <td>2.009447e-14</td>\n",
       "      <td>5.456968e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>6.310511e-15</td>\n",
       "      <td>8.749163e-13</td>\n",
       "      <td>1.579341e-14</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.221523e-16</td>\n",
       "      <td>1.643130e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>19</td>\n",
       "      <td>10</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.55</th>\n",
       "      <td>1.978151e-11</td>\n",
       "      <td>2.349783e-14</td>\n",
       "      <td>5.820766e-11</td>\n",
       "      <td>0.133756</td>\n",
       "      <td>5.781185e-15</td>\n",
       "      <td>1.472049e-12</td>\n",
       "      <td>4.463381e-15</td>\n",
       "      <td>45.0</td>\n",
       "      <td>336.434581</td>\n",
       "      <td>2.492525e-18</td>\n",
       "      <td>...</td>\n",
       "      <td>0.577997</td>\n",
       "      <td>44.87164</td>\n",
       "      <td>8.187520e-16</td>\n",
       "      <td>1.909584e-14</td>\n",
       "      <td>21.574149</td>\n",
       "      <td>39.491215</td>\n",
       "      <td>3.396464</td>\n",
       "      <td>21</td>\n",
       "      <td>11</td>\n",
       "      <td>-1000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>11 rows × 35 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                Fx            Fy            Fz      Mach            Mx  \\\n",
       "time                                                                     \n",
       "0.05  1.716671e-11  2.641222e-16  2.182787e-11  0.133756  2.459194e-14   \n",
       "0.10  1.739409e-11  1.000965e-15  2.364686e-11  0.133756  1.976768e-14   \n",
       "0.15  1.739409e-11  2.337016e-15  2.728484e-11  0.133756  1.678983e-14   \n",
       "0.20  1.762146e-11  3.932746e-15  2.910383e-11  0.133756  1.365093e-14   \n",
       "0.25  1.762146e-11  5.945782e-15  3.637979e-11  0.133756  1.163916e-14   \n",
       "0.30  1.807621e-11  8.315261e-15  4.001777e-11  0.133756  1.020804e-14   \n",
       "0.35  1.841727e-11  1.098849e-14  4.365575e-11  0.133756  9.148544e-15   \n",
       "0.40  1.875833e-11  1.383942e-14  4.729372e-11  0.133756  7.977795e-15   \n",
       "0.45  1.887202e-11  1.687040e-14  5.275069e-11  0.133756  7.010262e-15   \n",
       "0.50  1.944045e-11  2.009447e-14  5.456968e-11  0.133756  6.310511e-15   \n",
       "0.55  1.978151e-11  2.349783e-14  5.820766e-11  0.133756  5.781185e-15   \n",
       "\n",
       "                My            Mz   TAS           a       aileron   ...     \\\n",
       "time                                                               ...      \n",
       "0.05 -1.360312e-11  8.035347e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.10 -1.164692e-11  7.251039e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.15 -9.240578e-12  6.009923e-16  45.0  336.434581  2.492525e-18   ...      \n",
       "0.20 -6.789590e-12  1.213662e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.25 -5.474300e-12  1.650906e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.30 -3.640737e-12  2.051842e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.35 -2.045869e-12  1.306538e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.40 -1.049373e-12  7.766174e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "0.45  1.565743e-13  1.094014e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.50  8.749163e-13  1.579341e-14  45.0  336.434581  2.492525e-18   ...      \n",
       "0.55  1.472049e-12  4.463381e-15  45.0  336.434581  2.492525e-18   ...      \n",
       "\n",
       "        thrust         u             v        v_down     v_east    v_north  \\\n",
       "time                                                                         \n",
       "0.05  0.577997  44.87164  8.371463e-16  1.332268e-15  21.574149  39.491215   \n",
       "0.10  0.577997  44.87164  8.369266e-16  2.664535e-15  21.574149  39.491215   \n",
       "0.15  0.577997  44.87164  8.365954e-16  3.552714e-15  21.574149  39.491215   \n",
       "0.20  0.577997  44.87164  8.357530e-16  4.884981e-15  21.574149  39.491215   \n",
       "0.25  0.577997  44.87164  8.346854e-16  6.661338e-15  21.574149  39.491215   \n",
       "0.30  0.577997  44.87164  8.330276e-16  7.993606e-15  21.574149  39.491215   \n",
       "0.35  0.577997  44.87164  8.307814e-16  9.769963e-15  21.574149  39.491215   \n",
       "0.40  0.577997  44.87164  8.281022e-16  1.199041e-14  21.574149  39.491215   \n",
       "0.45  0.577997  44.87164  8.252482e-16  1.421085e-14  21.574149  39.491215   \n",
       "0.50  0.577997  44.87164  8.221523e-16  1.643130e-14  21.574149  39.491215   \n",
       "0.55  0.577997  44.87164  8.187520e-16  1.909584e-14  21.574149  39.491215   \n",
       "\n",
       "             w  x_earth  y_earth  z_earth  \n",
       "time                                       \n",
       "0.05  3.396464        1        1    -1000  \n",
       "0.10  3.396464        3        2    -1000  \n",
       "0.15  3.396464        5        3    -1000  \n",
       "0.20  3.396464        7        4    -1000  \n",
       "0.25  3.396464        9        5    -1000  \n",
       "0.30  3.396464       11        6    -1000  \n",
       "0.35  3.396464       13        7    -1000  \n",
       "0.40  3.396464       15        8    -1000  \n",
       "0.45  3.396464       17        9    -1000  \n",
       "0.50  3.396464       19       10    -1000  \n",
       "0.55  3.396464       21       11    -1000  \n",
       "\n",
       "[11 rows x 35 columns]"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results = sim.propagate(sim.time+dt)\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that `results` will include the previous timesteps as well as the last one. To get just the last one one can use pandas `loc` or `iloc`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fx             1.978151e-11\n",
       "Fy             2.349783e-14\n",
       "Fz             5.820766e-11\n",
       "Mach           1.337556e-01\n",
       "Mx             5.781185e-15\n",
       "My             1.472049e-12\n",
       "Mz             4.463381e-15\n",
       "TAS            4.500000e+01\n",
       "a              3.364346e+02\n",
       "aileron        2.492525e-18\n",
       "alpha          7.554882e-02\n",
       "beta           1.819449e-17\n",
       "elevator      -4.895112e-02\n",
       "height         1.000000e+03\n",
       "p              5.629520e-18\n",
       "phi            2.023926e-18\n",
       "pressure       8.987627e+04\n",
       "psi            5.000000e-01\n",
       "q             -1.670347e-15\n",
       "q_inf          1.125555e+03\n",
       "r              2.473422e-18\n",
       "rho            1.111660e+00\n",
       "rudder        -1.036751e-17\n",
       "temperature    2.816510e+02\n",
       "theta          7.554882e-02\n",
       "thrust         5.779967e-01\n",
       "u              4.487164e+01\n",
       "v              8.187520e-16\n",
       "v_down         1.909584e-14\n",
       "v_east         2.157415e+01\n",
       "v_north        3.949122e+01\n",
       "w              3.396464e+00\n",
       "x_earth        2.100000e+01\n",
       "y_earth        1.100000e+01\n",
       "z_earth       -1.000000e+03\n",
       "Name: 0.55, dtype: float64"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.iloc[-1]  # last time step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fx             1.978151e-11\n",
       "Fy             2.349783e-14\n",
       "Fz             5.820766e-11\n",
       "Mach           1.337556e-01\n",
       "Mx             5.781185e-15\n",
       "My             1.472049e-12\n",
       "Mz             4.463381e-15\n",
       "TAS            4.500000e+01\n",
       "a              3.364346e+02\n",
       "aileron        2.492525e-18\n",
       "alpha          7.554882e-02\n",
       "beta           1.819449e-17\n",
       "elevator      -4.895112e-02\n",
       "height         1.000000e+03\n",
       "p              5.629520e-18\n",
       "phi            2.023926e-18\n",
       "pressure       8.987627e+04\n",
       "psi            5.000000e-01\n",
       "q             -1.670347e-15\n",
       "q_inf          1.125555e+03\n",
       "r              2.473422e-18\n",
       "rho            1.111660e+00\n",
       "rudder        -1.036751e-17\n",
       "temperature    2.816510e+02\n",
       "theta          7.554882e-02\n",
       "thrust         5.779967e-01\n",
       "u              4.487164e+01\n",
       "v              8.187520e-16\n",
       "v_down         1.909584e-14\n",
       "v_east         2.157415e+01\n",
       "v_north        3.949122e+01\n",
       "w              3.396464e+00\n",
       "x_earth        2.100000e+01\n",
       "y_earth        1.100000e+01\n",
       "z_earth       -1.000000e+03\n",
       "Name: 0.55, dtype: float64"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.loc[sim.time]  # results for current simulation time"
   ]
  }
 ],
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